Peak shape estimation device and peak shape estimation method

Abstract

The present application relates to a peak shape estimation device, comprising: an acquisition unit that acquires measurement waveform data showing changes in measurement data in the domain direction from measurement data acquired over time in an analysis device; and an estimation unit that acquires estimation waveform data in which at least part of the noise data has been removed from the measurement waveform data. The estimation unit acquires the estimation waveform data with the noise data included in the measurement waveform data as data having a correlation with respect to the domain direction. Thus, the peak shape can be correctly estimated from the measurement waveform data to which noise has been added.

Description

Technical Field

[0001] This invention relates to an apparatus and method for estimating peak shape based on measured waveform data. Background Technology

[0002] Analytical devices such as chromatographs or mass analyzers output waveform data as analytical results. Qualitative analysis of the analyte is performed based on the position of the peaks appearing in the waveform data. Furthermore, quantitative analysis of the sample is performed based on the shape of the peaks appearing in the waveform data.

[0003] In estimating the peak shape appearing in waveform data, peak waveform models such as the Gaussian function, the EMG (Exponentially Modified Gaussian) function, and the BEMG (Bidirectional Exponentially Modified Gaussian) function are used. Patent Document 1 and Non-Patent Document 1 disclosed below disclose methods for estimating peak shapes using the BEMG function.

[0004] Existing technical documents

[0005] Patent documents

[0006] Patent Document 1: Japanese Patent No. 6260709

[0007] Non-patent literature

[0008] Non-Patent Literature 1: Arase, Shuntaro et al., “Intelligent peak deconvolution through in-depth study of the data matrix from liquid chromatography coupled with a photo-diode array detector applied to pharmaceutical analysis,” Journal of Chromatography, 2016, v. 1469, pp. 35-47. Summary of the Invention

[0009] The technical problem that the invention aims to solve

[0010] In waveform data output from an analysis device, there may be additional noise or overlapping peaks. In such cases, it is sometimes impossible to accurately observe the peak shape based on the waveform data. One method for estimating peak shape from waveform data with added noise is to add error terms to the peak waveform model. For example, in the least squares method, an error term is added to the peak waveform model assuming that there is noise that is independent of the observation time and follows a normal distribution. Then, the error term is removed by calculating the parameter values ​​of the peak waveform model using optimization and sequential algorithms such as Markov chain Monte Carlo (MCMC), thus estimating the true peak shape.

[0011] However, it is known that, under the assumption that the waveform data contains noise that is independent of the observation time and follows a normal distribution, local solutions caused by peak tailing are generated in the peak shape estimation process. If local solutions are generated, the peak shape estimation cannot always be performed correctly because optimization and sampling cannot be performed efficiently.

[0012] The object of this invention is to accurately estimate the peak shape based on waveform data with added noise.

[0013] Solution to the above technical problems

[0014] According to one aspect of the present invention, the peak shape estimation device is a computer-implemented peak shape estimation device having a computing unit, the computing unit comprising: an acquisition unit that acquires measurement waveform data showing the change of the measurement data in the defined domain direction from measurement data acquired over time in an analysis device; and an estimation unit that acquires estimated waveform data from the measurement waveform data after at least partially removing noise data, the estimation unit acquiring the estimated waveform data by treating the noise data contained in the measurement waveform data as data having a correlation in the defined domain direction.

[0015] Invention Effects

[0016] According to the present invention, the peak shape can be accurately estimated from waveform data with added noise. Attached Figure Description

[0017] Figure 1 This is a configuration diagram of the peak shape estimation device in this embodiment.

[0018] Figure 2 This is a functional block diagram of the peak shape estimation device in this embodiment.

[0019] Figure 3 It is a graph showing waveform data with and without tailed peaks.

[0020] Figure 4 This is a flowchart illustrating the peak shape estimation method of this embodiment.

[0021] Figure 5 It is a graph showing the observed waveform data and the peak shape inferred under the assumption that the noise follows a time series model.

[0022] Figure 6 It is a graph showing the observed waveform data and the actual peak shape.

[0023] Figure 7 It is a graph showing the observed waveform data and the peak shape inferred under the assumption that the noise is independent over the observation time.

[0024] Figure 8 It is a violin plot showing the area distribution of the estimated peak. Detailed Implementation

[0025] Next, the peak shape estimation apparatus and peak shape estimation method of the present invention will be described with reference to the accompanying drawings.

[0026] (1) Composition of the peak shape estimation device

[0027] Figure 1 This is a configuration diagram of the peak shape estimation device 1 in the embodiment. The peak shape estimation device 1 is, for example, a computer such as a personal computer. The peak shape estimation device 1 of this embodiment acquires measurement data of a sample obtained in a liquid chromatograph, gas chromatograph, or mass analysis device. Furthermore, the peak shape estimation device 1 is a device for estimating the peak shape based on the measurement data of the sample.

[0028] like Figure 1 As shown, the peak shape estimation device 1 includes a CPU (Central Processing Unit) 11, RAM (Random Access Memory) 12, ROM (Read Only Memory) 13, an operation unit 14, a display 15, a storage device 16, a communication interface (I / F) 17, and a device interface (I / F) 18.

[0029] CPU 11 performs overall control of peak shape estimation device 1. RAM 12 is used as a working area when CPU 11 executes a program. Control programs and the like are stored in ROM 13. Operation unit 14 accepts input operations performed by the user. Operation unit 14 includes a keyboard and mouse. Display 15 displays information such as analysis results.

[0030] Storage device 16 is a storage medium such as a hard disk. Storage device 16 stores estimation program P1, measured waveform data MD, estimated waveform data ED, and peak waveform model ML.

[0031] The estimation program P1 performs estimation processing on the measured waveform data MD and outputs the estimated waveform data ED. The measured waveform data MD may contain added noise or multiple overlapping peaks. The estimation program P1 obtains the estimated waveform data ED, which represents the true peak shape, by performing estimation processing on the measured waveform data MD. During the estimation processing, the estimation program P1 applies the measured waveform data MD to the peak waveform model ML. The peak waveform model ML includes Gaussian functions, EMG (Exponentially Modified Gaussian) functions, and BEMG (Bidirectional Exponentially Modified Gaussian) functions, etc.

[0032] Communication interface 17 is an interface for wired or wireless communication with other computers. Device interface 18 is an interface for accessing storage media 19 such as CDs, DVDs, and semiconductor memories.

[0033] (2) Functional composition of peak shape estimation device

[0034] Figure 2 This is a block diagram illustrating the functional configuration of the peak shape estimation device 1. Figure 2 In this configuration, the control unit 20 is a functional unit implemented by the CPU 11 using the RAM 12 as a working area and executing the estimation program P1. The control unit 20 includes an acquisition unit 21, an estimation unit 22, a peak display unit 23, and an area calculation unit 24. That is, the acquisition unit 21, the estimation unit 22, the peak display unit 23, and the area calculation unit 24 are functional units implemented by executing the estimation program P1. In other words, the acquisition unit 21, the estimation unit 22, the peak display unit 23, and the area calculation unit 24 can also be considered as functional units possessed by the CPU 11.

[0035] The acquisition unit 21 inputs measurement data AD. For example, the acquisition unit 21 inputs measurement data AD from another computer via the communication interface 17. Alternatively, the acquisition unit 21 inputs measurement data AD stored in the storage medium 19 via the device interface 18. Measurement data AD is analytical data of a sample acquired over time in a liquid chromatograph, gas chromatograph, or mass analysis device. When measurement data AD is analytical data obtained in a chromatograph, it is three-dimensional chromatogram data with three dimensions: time, wavelength, and absorbance (signal intensity). When measurement data AD is analytical data obtained in a mass analysis device, it is mass analysis data with three dimensions: time, mass-to-charge ratio, and ionic strength (signal intensity).

[0036] The acquisition unit 21 extracts measurement waveform data MD from the input measurement data AD and saves the measurement waveform data MD in the storage device 16. The measurement waveform data MD is two-dimensional data extracted from the measurement data AD. For example, the measurement waveform data MD is two-dimensional chromatogram data showing the relationship between time and absorbance. Alternatively, the measurement waveform data MD is two-dimensional mass analysis data showing the relationship between time and ion intensity.

[0037] The estimation unit 22 reads the measured waveform data MD and the peak waveform model ML, and applies the measured waveform data MD to the peak waveform model ML. The estimation unit 22 performs Bayesian estimation by using the peak waveform model ML as a prior distribution to obtain the estimated waveform data ED.

[0038] Peak display unit 23 outputs the estimated waveform data ED estimated in estimation unit 22 to display unit 15. Area calculation unit 24 calculates the peak area of ​​the estimated waveform data ED estimated in estimation unit 22. Area calculation unit 24 also outputs a violin plot of the calculated peak area to display unit 15.

[0039] (3) Noise and peak overlap

[0040] Next, the noise and overlapping of multiple peaks contained in the measured waveform data MD will be explained. Figure 3 This is a graph showing the measured waveform data MD. Figure 3 In the diagram, waveform W1 shows a peak shape without tailing, and waveform W2 shows a peak shape with tailing. Furthermore, waveform W3 is a residue of waveforms W1 and W2. Even if waveform W3 contains overlapping peaks of impurities, interpreting the waveform obtained by adding these overlaps as impurities will not make the analysis results unnatural. It is known that when the error term added to the peak waveform model is treated as noise that is independent of the observation time and follows a normal distribution, local solutions caused by peak tailing are generated, preventing high-precision optimization and sampling. That is, it is difficult to distinguish between a waveform with tailing on a single peak and a waveform with a large error added to a shoulder peak without tailing. Furthermore, it is difficult to distinguish between a waveform with tailing on a single peak and a waveform with overlapping peaks of other components.

[0041] The inventors of this application discovered that such estimation errors occur because noise that is interdependent in the time direction, such as trailing noise, is treated as Gaussian noise that is independent in the observation time. Therefore, the peak shape estimation device 1 of this embodiment improves the estimation accuracy of the peak shape by processing the noise as data following a time series model.

[0042] (4) Peak shape estimation method

[0043] Next, the peak shape estimation method of this embodiment will be described. Figure 4 This is a flowchart illustrating the peak shape estimation method of this embodiment. First, in step S1, the acquisition unit 21 (refer to...) Figure 2 Input measurement data AD, and obtain measurement waveform data MD based on the measurement data AD. Here, as an example, the measurement data AD is set as three-dimensional chromatogram data with three dimensions: time, waveform, and absorbance (signal intensity), obtained from a liquid chromatograph. In addition, the measurement waveform data MD is set as two-dimensional chromatogram data showing the relationship between time and absorbance.

[0044] Next, in step S2, the estimation unit 22 (refer to...) Figure 2 The measured waveform data MD is read, and the estimated waveform data ED is obtained using the peak waveform model ML. At this time, the estimation unit 22 adds noise data following the time series model to the peak waveform model ML as an error term.

[0045] In this embodiment, the estimation unit 22 uses the BEMG (Bidirectional Exponentially Modified Gaussian) function as the peak waveform model ML. Furthermore, the estimation unit 22 performs Bayesian estimation by using the peak waveform model ML as a prior distribution to obtain the estimated waveform data ED. Equation 1 illustrates the BEMG function.

[0046] [Number 1]

[0047]

[0048] In equation number 1, u is a parameter related to the peak position, s is a parameter related to the peak width, a is a parameter related to the leading edge, and b is a parameter related to the tailing.

[0049] Since the measured waveform data MD can be regarded as data obtained by peak overlap represented by the BEMG function, it is presumed that the waveform data ED can be represented as in equation 2.

[0050] [Number 2]

[0051]

[0052] In equation 2, K is the number of overlapping peaks. Ai is the coefficient of each peak. Noise[t] is the error term. In this embodiment, the estimation unit 22 treats Noise[t] as an error term as following a time series model. Equation 3 shows the error term.

[0053] [Number 3]

[0054]

[0055] Noise[t], expressed by equation 3, represents the error term for the t-th observation point, ordered by the elution sequence from the start of the observation. Furthermore, N(0, σ) 2 The figure shows the mean 0 and variance σ. 2 The distribution follows a normal pattern. Furthermore, θ represents the autocorrelation coefficient. These θ, σ... 2 The initial error term Noise[1] is set to an optimal value by the user. That is, Noise[t] has an error component (θ×Noise[t-1]) that is correlated in the time direction and an error component (ε) that is independent in time. t Thus, in this embodiment, the estimation unit 22 uses a time series model called an autoregressive model of order 1 as the error term.

[0056] The estimation unit 22 uses the peak waveform model ML and error term shown in equations 1 to 3 to perform sequential algorithms such as optimization or Markov chain Monte Carlo (MCMC) to obtain the estimated waveform data ED. The estimation unit 22 stores the acquired estimated waveform data ED in the storage device 16. Figure 5 This is a diagram showing the estimated waveform data ED acquired by the estimation unit 22. Furthermore, Figure 6 It is shown that... Figure 5 The diagram shows the actual waveform data corresponding to the estimated waveform data ED. Figure 6 The actual waveform data shown is, for example, a waveform obtained by setting appropriate parameters for the BEMG function.

[0057] exist Figure 5 In the estimated waveform data ED, estimated peak 1 and estimated peak 2 are included. Figure 6 The image contains true peak 1 and true peak 2. Figure 5 and Figure 6 In the diagram, × represents the measured waveform data MD. Figure 5 In the waveform, the width of each peak is due to the probability distribution of the inferred waveform data ED, which is inferred through Bayesian estimation. Furthermore, Figure 5 The estimated waveform data ED is the result of 100 independent estimation processes performed by changing the initial value (Noise in Equation 3[1]). Therefore, each peak waveform also has a width, based on the estimation results described 100 times. Although each peak waveform has a width, they depict roughly the same peak shape. Therefore, it can be seen that the estimated waveform data ED performed the estimation process independently of the initial value.

[0058] If reference Figure 5 and Figure 6Therefore, it can be seen that the estimated peaks 1 and 2 do not deviate significantly from the actual peaks 1 and 2, indicating that the estimations were performed with high precision. Furthermore, if we refer to... Figure 5 It can be seen that there is no unnatural deviation between the estimated waveform data ED and the measured waveform data MD shown in ×, and the estimation was performed with high accuracy. Thus, the peak shape estimation device 1 of this embodiment can remove noise data from the measured waveform data MD with high accuracy. Of course, although it is desirable to completely remove the original noise, according to the peak shape estimation device 1 of this embodiment, the true peak can be estimated by removing the original noise with high accuracy at least partially.

[0059] Figure 7 This illustrates waveform data obtained by estimating the peak shape using conventional methods for the same measured waveform data MD. Conventional methods involve estimating the peak shape based on the assumption that the measured waveform data MD is supplemented with noise that is independent of the observation time and follows a normal distribution. Figure 7 The shapes of two peaks, presumed peak 1 and presumed peak 2, were determined. Figure 7 The waveform shown by the dashed line is presumed peak 1, and the waveform shown by the solid line is presumed peak 2. Figure 7 In the diagram, the points indicated by the black circles and the lines connecting them represent the waveform obtained by adding estimated peak 1 and estimated peak 2. That is, the lines connecting the black circles represent the estimated waveform data without error terms. Additionally, the lines indicated by ×... Figure 5 and Figure 6 Similarly, for measuring waveform data MD. For example... Figure 7 As shown, if the estimated waveform data shown by the line connecting the black circles is compared with the measured waveform data MD, it can be seen that there is an unnatural deviation in the shoulder of the peak, and the wavy behavior of the measured waveform data MD is ignored.

[0060] produce Figure 7 The results show that the error term takes consecutively large values. That is, the error terms at adjacent points are correlated. However, in Figure 7 In the example shown, it is assumed that the error term is independent at each point, so no restrictions are placed on the correlation between adjacent points. Therefore, it can be seen that the wavy behavior is also treated as Gaussian noise that is independent at each point.

[0061] In contrast, in the peak shape estimation apparatus 1 of this embodiment, an autoregressive process model, which is a time series model, is used in the estimation of the error term. That is, a correlation between the error term and adjacent points is assumed. Therefore, it is possible to generate... Figure 5 and Figure 6 The model shown incorporates a relatively strong error term. Therefore, it can be assumed that the local and global solutions are smoothly connected, and when updating parameters using a sequential algorithm, it is easy to move between the local and global solutions.

[0062] Return to Figure 4 The flowchart. Next, in step S3, the area calculation unit 24 (refer to...) Figure 2 The peak areas are calculated for estimated peak 1 and estimated peak 2. In this embodiment, the estimated waveform data ED has a probability distribution because it is estimated through Bayesian estimation. Therefore, the peak areas calculated by the area calculation unit 24 also have a probability distribution.

[0063] Next, in step S4, the peak display unit 23 and the area calculation unit 24 (see reference) Figure 2 The estimated result will be displayed on the monitor 15. The peak display unit 23 will display the result as shown. Figure 5 The peak shape of the estimated waveform data ED is displayed on the display 15. At the same time, the peak display unit 23 also displays the measured waveform data MD. Figure 5 The data shown in the figure can be visually verified to confirm the accuracy of the estimated processing.

[0064] In addition, the area calculation unit 24 displays the estimated peak area on the display 15. Figure 8 A violin plot of the peak area displayed on the display 15 by the area calculation unit 24 is shown. Figure 8 In the diagram, the vertical axis represents the peak area, and the horizontal axis symmetrically depicts the probability density of presumed peak 1 or presumed peak 2. It can be seen that the peak area of ​​presumed peak 1 is centered around 1.000, while the peak area of ​​presumed peak 2 is centered around 0.400. Users can visually confirm the accuracy of the presumed processing by referring to this peak area presumption information.

[0065] (6) The correspondence between each element of the claims and each element of the embodiments.

[0066] Hereinafter, examples of the correspondence between the constituent elements of the claims and the elements of the embodiments will be described, but the present invention is not limited to the examples described below. In the above embodiments, CPU11 is an example of an arithmetic unit. In the above embodiments, a liquid chromatograph, a gas chromatograph, or a mass analysis apparatus is an example of an analytical apparatus. Furthermore, in the above embodiments, the time direction is an example of a domain direction.

[0067] As constituent elements of the claims, various elements having the structure or function described in the claims can also be used.

[0068] (7) Other implementation methods

[0069] In the above embodiment, two peaks can be separated by peak estimation processing. This is just one example; the peak shape estimation device 1 of this embodiment can also separate three or more peaks by performing the same estimation processing as described above.

[0070] In the above implementation, the error term is treated as a time series model, utilizing a first-order autoregressive process model. Besides this, other time series models representing the error term can include second-order or higher autoregressive process models, moving average process models, autoregressive moving average process models, autoregressive integral moving average process models, state-space models, and any combination of these models.

[0071] In the above embodiment, the error term was treated as a model with a correlation in the time direction. The peak shape estimation device 1 of this embodiment can also be applied to cases where the error term is correlated with parameters other than time. That is, when the signal strength is obtained for the domain of a certain parameter, the present invention can be applied when the error term is correlated with respect to the domain direction.

[0072] In the above embodiments, the peak shape is estimated based on the premise that the error terms have a correlation in the domain direction. That is, the peak shape is estimated by adding the error terms shown in Equation 3 to the peak waveform model ML shown in Equation 1. As another application example of the present invention, by using the same method to estimate the peak shape, it can also be used as an anomaly detection device.

[0073] In the error term shown in Equation 3, θ represents the autocorrelation coefficient. Typically, in the absence of time-series noise and only time-independent noise, θ should be a very small value close to zero. A large value of θ can be considered a situation where incorrect analysis conditions or other factors prevent normal analysis from being performed. For example, by treating a large value of θ exceeding a threshold as an anomaly detection, the apparatus and method of the present invention can be applied as an anomaly detection apparatus and method.

[0074] In the above embodiment, the case where the estimation program P1 is stored in the storage device 16 is described as an example. In other embodiments, the estimation program P1 may also be provided stored in the storage medium 19. Alternatively, the CPU 11 of the peak shape estimation device 1 may access the storage medium 19 via the device interface 18 and save the estimation program P1 stored in the storage medium 19 to the storage device 16 or the ROM 13. Alternatively, the CPU 11 may access the storage medium 19 via the device interface 18 and execute the estimation program P1 stored in the storage medium 19.

[0075] Furthermore, the specific configuration of the present invention is not limited to the above-described embodiments, and various changes and modifications can be made without departing from the spirit of the invention.

[0076] (8) Scheme

[0077] Those skilled in the art will understand that the above-described exemplary embodiments are specific examples of the following solutions.

[0078] (Item 1)

[0079] One aspect of the present invention provides a peak shape estimation device implemented by a computer equipped with a computation unit.

[0080] The arithmetic unit includes:

[0081] The acquisition unit acquires measurement waveform data, which shows the change of the measurement data in the defined domain direction, from the measurement data acquired over time in the analysis device.

[0082] The estimation unit obtains at least partially noise-removed estimated waveform data from the measured waveform data.

[0083] The estimation unit obtains the estimated waveform data by treating the noise data contained in the measured waveform data as data that has a correlation in the defined domain direction.

[0084] It is possible to accurately estimate the noise-removed waveform data based on the measured waveform data with added noise. Therefore, it is possible to accurately estimate the peak shape of the noise-removed waveform.

[0085] (Item 2)

[0086] In the peak shape estimation device described in item 1,

[0087] The estimation section may also attach a time series model as noise data to a peak waveform model that estimates the peak shape contained in the measured waveform data.

[0088] It can accurately estimate the peak shape based on the measured waveform data containing noise that is correlated in the time direction.

[0089] (Item 3)

[0090] In the peak shape estimation device described in item 2,

[0091] The time series model can be selected from a group of models consisting of autoregressive process models, moving average process models, autoregressive moving average process models, autoregressive integral moving average process models, state-space models, and any combination thereof.

[0092] Noise that is correlated in the time direction can be inferred.

[0093] (Item 4)

[0094] In any of the peak shape estimation devices described in items 1 to 3,

[0095] The arithmetic unit may further include an area calculation unit that calculates the peak area using the estimated waveform data.

[0096] Users can visually verify the estimated accuracy by referring to the peak area.

[0097] (Item 5)

[0098] In any of the peak shape estimation devices described in items 1 to 4,

[0099] The estimation unit can use Bayesian estimation to obtain the estimated waveform data.

[0100] The probability distribution of the inferred waveform data can be obtained through Bayesian inference.

[0101] (Item 6)

[0102] Another aspect of the present invention is a peak shape estimation device implemented by a computer equipped with a computing unit.

[0103] The arithmetic unit includes:

[0104] The acquisition unit acquires measurement waveform data, which shows the change of the measurement data in the defined domain direction, from the measurement data acquired over time in the analysis device.

[0105] The estimation unit estimates the noise data contained in the measured waveform data.

[0106] The estimation unit processes the noise data contained in the measured waveform data as data that has a correlation with the domain direction, and detects an anomaly when the correlation coefficient of the noise data in the domain direction exceeds a predetermined threshold.

[0107] It can detect and analyze anomalies in conditions by utilizing the correlation of noise.

[0108] (Item 7)

[0109] Another aspect of the peak shape estimation method of the present invention includes:

[0110] The acquisition process involves acquiring measurement waveform data, which shows the variation of the measurement data in the defined domain direction, from the measurement data acquired over time in the analysis device.

[0111] The estimation step involves obtaining at least partially noise-removed estimated waveform data from the measured waveform data.

[0112] The estimation process uses the noise data contained in the measured waveform data as data that has a correlation with the direction of the defined domain to obtain the estimated waveform data.

[0113] (Item 8)

[0114] Another aspect of the peak shape estimation method of the present invention includes:

[0115] The acquisition process involves acquiring measurement waveform data, which shows the variation of the measurement data in the defined domain direction, from the measurement data acquired over time in the analysis device.

[0116] The estimation process estimates the noise data contained in the measured waveform data.

[0117] The estimation process treats the noise data contained in the measured waveform data as data that has a correlation with the domain direction, and detects anomalies when the correlation coefficient of the noise data in the domain direction exceeds a specified threshold.

Claims

1. A peak shape estimation device, which is a peak shape estimation device implemented by a computer equipped with a computing unit, characterized in that, The arithmetic unit includes: The acquisition unit acquires measurement waveform data showing the change of the measurement data in the time direction from the measurement data acquired over time in the analysis device. The estimation unit obtains at least partially noise-removed estimated waveform data from the measured waveform data. The estimation unit uses a peak waveform model with an added error term that is correlated in the time direction to estimate the peak shape contained in the measured waveform data, thereby obtaining the estimated waveform data.

2. The peak shape estimation device as described in claim 1, characterized in that, The estimation unit appends the time series model as the noise data to the peak waveform model.

3. The peak shape estimation device as described in claim 2, characterized in that, The time series model is selected from a group of models consisting of autoregressive process models, moving average process models, autoregressive moving average process models, autoregressive integral moving average process models, state-space models, and any combination thereof.

4. The peak shape estimation device as described in claim 1, characterized in that, The arithmetic unit further includes an area calculation unit that calculates the peak area using the estimated waveform data.

5. The peak shape estimation device as described in claim 1, characterized in that, The estimation unit uses Bayesian estimation to obtain the estimated waveform data.

6. A peak shape estimation device, which is a peak shape estimation device implemented by a computer equipped with a computing unit, characterized in that, The arithmetic unit includes: The acquisition unit acquires measurement waveform data, which shows the change of the measurement data in the defined domain direction, from the measurement data acquired over time in the analysis device. The estimation unit estimates the noise data contained in the measured waveform data. The estimation unit processes the noise data contained in the measured waveform data as data that has a correlation with the domain direction, and detects an anomaly when the correlation coefficient of the noise data in the domain direction exceeds a predetermined threshold.

7. A method for estimating peak shape, characterized in that, include: The acquisition process involves acquiring measurement waveform data, which shows the change of the measurement data in the time direction, from the measurement data acquired over time in the analysis device. The estimation step involves obtaining at least partially noise-removed estimated waveform data from the measured waveform data. The estimation process uses a peak waveform model with an added error term that is correlated in the time direction to estimate the peak shape contained in the measured waveform data, thereby obtaining the estimated waveform data.

8. A method for estimating peak shape, characterized in that, include: The acquisition process involves acquiring measurement waveform data, which shows the variation of the measurement data in the defined domain direction, from the measurement data acquired over time in the analysis device. The estimation process estimates the noise data contained in the measured waveform data. The estimation process treats the noise data contained in the measured waveform data as data that has a correlation with the domain direction, and detects anomalies when the correlation coefficient of the noise data in the domain direction exceeds a specified threshold.

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