JP2018025971A - Data smoothing method and program for implementing the same - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a data smoothing method that offers better repeatability than conventional methods.SOLUTION: A data smoothing method of the present invention involves computing standard error of numerical data or data based thereon at each data acquisition point, and determining a smoothing width based on the standard error such that the greater the standard error of data acquisition points, the smaller the smoothing width. The numerical data or data based thereon at each data acquisition point is smoothed using the determined smoothing width.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a smoothing process of data acquired at a constant period, such as measurement data acquired by a detector of an analyzer.

  For example, in a detector used in a liquid chromatograph, a gas chromatograph or the like, a signal intensity for each fixed time is obtained as numerical data, and a chromatogram of a sample is obtained by graphing it. Since the numerical data of the signal obtained by the detector contains various types of noise, a smoothing process that smoothes the numerical data and reduces the influence of noise is used to more accurately grasp the trend of the signal waveform. This is often done (for example, see Patent Document 1).

  In such smoothing processing of discrete data, a method is often used in which a smooth value of one point is calculated by a convolution operation between data near both sides of the point and a weight function. There are various weighting functions such as a simple averaging function and a Gaussian function. As a similar method, there are a method of approximating neighboring data with a polynomial to obtain a smooth value (Savitzky-Golay method) and an adaptive smoothing method.

JP 2006-242750 A

  The number of data near the both sides used for smoothing (hereinafter referred to as smoothing width) has a smoothing width sufficient to suppress noise components near the baseline when the data consists of a baseline and a peak. There is a need. Since the smoothing width is usually fixed in the smoothing target area, if smoothing processing is performed on the peak data having a width close to the smoothing width or the peak portion having a width narrower than the smoothing width, Distortion (a value smaller than the original data) occurs in the data near the vertex. In addition to affecting the calculation of the peak height and peak area, this distortion may not separate the peaks when the peaks are close to each other. That is, with the conventional smoothing method, there may be a problem in data reproducibility depending on the type of data.

  Therefore, an object of the present invention is to provide a data smoothing method with improved reproducibility compared with a conventional method.

In the data smoothing method according to the present invention, the numerical data acquired at a plurality of data acquisition points or the data based thereon is the numerical value of the data acquisition points within the smoothing width including the data acquisition point at which each numerical data is acquired. This is a data smoothing method for smoothing using data or data based thereon.
This data smoothing method is
A standard error calculating step for calculating a standard error of the numerical data of each data acquisition point or data based thereon; and
After the standard error calculation step, the smoothing width of each data acquisition point is set so that the smoothing width becomes narrower as the data acquisition point has a larger standard error of numerical data or data based thereon. A smoothing width determining step for determining based on the standard error of the numerical data or data based thereon;
A smoothing step of performing a smoothing process of the numerical data of each data acquisition point or data based thereon using the numerical data of the data acquisition point within the smoothing width determined in the smoothing width determination step or data based thereon And.

  The “data acquisition point” means a point at which numerical data is acquired. For example, in the case of data acquired at regular intervals, it means each time at which numerical data is acquired.

  The details of the “standard error” will be described later, but by obtaining the “standard error” of the numerical data of each data acquisition point or the data based on it, the magnitude of the fluctuation of the data at that data acquisition point (change in the slope of the data ). Therefore, by obtaining the standard error, it is possible to numerically determine the base line portion in the data series and the region where the change in the slope of data such as a peak is large (the absolute value of the second derivative is large).

  In the data smoothing method of the present invention, in the smoothing width determination step, the smoothing width of each data acquisition point is calculated based on the standard error calculated in the standard error calculation step and a smoothing width table prepared in advance. It may be determined. Then, it is easy to determine the smoothing width.

  And a normalizing step for normalizing the standard error calculated in the standard error calculating step by a predetermined calculation method after the standard error calculating step and before the smoothing width determining step. In the step, the smoothing width of each data acquisition point may be determined based on the standard error normalized in the normalizing step and a smoothing width table prepared in advance.

  The program according to the present invention is configured to execute the above-described data smoothing method by being executed by a computer.

  In the data smoothing method according to the present invention, the standard error of the numerical data of each data acquisition point or data based thereon is calculated, and based on the standard error so that the smoothing width becomes narrower as the data acquisition point has a larger standard error. Since the smoothing width is determined, the smoothing width is large in areas where the change in the slope of the data is small (the absolute value of the second derivative is small), such as in the baseline portion, and the slope of the data, such as in the peak portion, is large. In the region where the change is large (the absolute value of the second derivative is large), the smoothing width is small. Thereby, it becomes possible to obtain smoothed data close to the original data, and the reproducibility is improved as compared with the conventional smoothing process.

  Since the program according to the present invention is configured to execute the smoothing method described above, smoothing processing with high reproducibility can be executed on a computer.

It is a flowchart which shows one Example of the data smoothing method. It is a graph which shows an example of the signal waveform before performing a smoothing process. It is a graph which shows the waveform of the standard error of each numerical data of the same signal waveform superimposed on the original waveform. It is a graph which shows the waveform after performing the smoothing process of each numerical data of the same signal waveform, and the original waveform. It is a graph which shows the waveform of the primary differential value of a melting curve, and the waveform of the standard error of each primary differential value as an example of the signal waveform before performing a smoothing process. It is a graph which shows the waveform which performed the smoothing process of the same-order differential value. It is a block diagram which shows an example of a structure of the computer by which the smoothing program was introduce | transduced.

  Hereinafter, an embodiment of a data smoothing method according to the present invention and a program for executing the method will be described.

  First, the outline of the smoothing method of this embodiment will be described with reference to the flowchart of FIG.

ここで、ｙ_iはデータ取得ポイントｉにおける数値データ、Ｙ_iはデータ取得ポイントｉにおける回帰直線による予測値、ｎは予め決められた標準誤差計算幅である。標準誤差計算幅とは、そのデータ取得ポイントの±Ａの範囲内のデータ取得ポイントの数値データを用いて標準誤差の計算を行なうということを意味する。すなわち、ｎ＝２Ａ＋１と表わすことができる。したがって、データ取得ポイントｉの標準誤差を計算するためには、（ｉ−Ａ）から（ｉ＋Ａ）までのデータ取得ポイントの数値データが用いられる。 The standard error of the numerical data acquired at each data acquisition point for every fixed period from the detector of the analyzer or data based thereon is calculated. The standard error can be obtained, for example, by dividing the residual sum of squares with respect to the regression line by the degree of freedom and taking the square root. If the regression line calculated from the numerical data is represented by Y = ax + b, the standard error SE can be obtained by the following equation (1).

Here, y _i is numerical data at the data acquisition point i, Y _i is a predicted value by a regression line at the data acquisition point i, and n is a predetermined standard error calculation width. The standard error calculation width means that the standard error is calculated using the numerical data of the data acquisition point within the range of ± A of the data acquisition point. That is, it can be expressed as n = 2A + 1. Therefore, in order to calculate the standard error of the data acquisition point i, the numerical data of the data acquisition points from (i−A) to (i + A) is used.

  After calculating the standard error of each data acquisition point, the standard error is normalized. The standard error normalization is performed by using a coefficient or the like prepared in advance so that the smoothing width can be determined by applying the standard error to a table for smoothing width determination prepared in advance. It is to correct to a predetermined scale. The standard error thus normalized is hereinafter referred to as “normalized standard error”.

  After normalizing the standard error, the normalized standard error is applied to a smoothing width determination table (hereinafter referred to as a smoothing width table) as shown in Tables 2 and 3 below, and each data acquisition point The smoothing width to be applied to the smoothing process is determined. The smoothing width is the numerical data of the data acquisition points within the range of ± B of the data acquisition point i, that is, from (i−B) to (i + B) in order to execute the smoothing process of the data acquisition point i. Means to use. Hereinafter, “B” indicating the width before and after the smoothing width is referred to as a smoothing half width.

  As apparent from Tables 2 and 3, the smoothing width is set smaller as the standard error (normalized standard error) is larger. A data acquisition point with a large standard error has a large fluctuation range of the slope of numerical data with respect to the data acquisition points before and after that, and smoothing with a smoothing width narrower than the numerical data of such data acquisition points By performing the processing, a value close to the original data is obtained as the smoothed data.

  After determining the smoothing width as described above, smoothing processing is performed on the numerical data at each data acquisition point using the smoothing width. There are various smoothing methods, any of which may be used, but one example is the Savitzky-Golay method. In the smoothing by the Savitzky-Golay method, the smoothing calculation is performed using the coefficients shown in the following Table 1.

In Table 1, the uppermost numerical value is the smoothing width (Width), and the second numerical value is the smoothing half width (Half width). Numerical values in the third and lower stages indicate coefficients used for smoothing calculation. For example, in the smoothing for the data acquisition point whose smoothing width is determined to be 7, the coefficients listed in the fourth column from the left are used, and the following expression (2) is formed. Using this equation (2), the numerical data is smoothed, and the smoothed data Y ′ _i is calculated.

[Example 1]
An example in which the smoothing process of the signal value waveform of FIG. 2 obtained by the detector of the analyzer is performed by the above smoothing method will be described.

(Calculation of standard error)
First, the standard error SE of the original numerical data obtained by the detector was calculated. The standard error SE here is a standard error with respect to a predicted value based on a regression line of 2A + 1 points in the vicinity, and is calculated using the above equation (1). When the standard error SE is displayed superimposed on the original numerical data, it is as shown in FIG. As can be seen from FIG. 3, the standard error SE at each data acquisition point represents the amount of change in the slope of the numerical data relative to the numerical data at the preceding and subsequent data acquisition points.

(Standard error normalization)
The standard error SE of the numerical data at each data acquisition point was normalized so that it could be applied to the smoothing width table of Table 2 prepared in advance, and the normalized standard error SE ′ was obtained.

(Determination of smoothing width)
Thereafter, a standard deviation S and an average M of the normalized standard error SE ′ in a predetermined baseline region were obtained. In this embodiment, the standard deviation S and the average M are used as criteria for determining the smoothing width. From the levels shown in the smoothing width table of Table 2, the level to which each normalized standard error SE ′ applies is extracted, and the smoothing half width is determined. Here, C is a smoothing width adjustment level, which is a value smaller than the smoothing half width B. d is a smoothing width adjustment constant, and is a value larger than zero.

(Smoothing process)
Using the normalized standard error SE ′ and the smoothing half width determined based on Table 2 above, the numerical data at each data acquisition point was smoothed by the Savitzky-Golay method described above. The result is shown in FIG. FIG. 4 is an enlarged view of the peak portion of the specific peak extracted from the waveform shown in FIG. 2. The original signal value waveform, the waveform smoothed by adjusting the smoothing width based on the standard error, the smoothing Waveforms obtained by smoothing with a fixed width fixed at 21 points are shown superimposed.

  As is clear from FIG. 4, when the smoothing width is fixed at 21 points and the smoothing process is performed, the peak waveform height is lower than the original signal value waveform, but smoothing is performed using the standard error. By adjusting the width, the reduction of the peak waveform height is suppressed, and a waveform close to the original peak waveform can be obtained.

[Example 2]
An example in which a melting curve measured for a substance is smoothed will be described.

(Calculation of standard error)
FIG. 5 shows the waveform of the value obtained by inverting the sign of the first derivative of the melting curve measured for a certain substance (data based on the original numerical data) and the waveform of its standard error SE. The standard error SE here is a standard error with respect to a predicted value based on a regression line of 2A + 1 points in the vicinity of each data acquisition point, and was calculated using the above equation (1).

(Standard error normalization)
The standard error SE of the numerical data at each data acquisition point was normalized so that it could be applied to the smoothing width table of Table 3 prepared in advance, and the normalized standard error SE ′ was obtained.

(Determination of smoothing width)
From the levels shown in the smoothing width table of Table 3, the level to which each normalized standard error SE ′ applies is extracted, and the smoothing half width is determined. Here, C is a smoothing width adjustment level, which is a value smaller than the smoothing half width B. d is a smoothing width adjustment constant, which is larger than (−1 / C) and smaller than (1 / C).

(Smoothing process)
Using the normalized standard error SE ′ and the smoothing half width determined based on Table 3 above, the numerical data at each data acquisition point was smoothed by the Savitzky-Golay method described above. The result is shown in FIG. In FIG. 6, a waveform smoothed by adjusting the smoothing width based on the standard error and a waveform smoothed by fixing the smoothing width to 21 points are superimposed.

  As is clear from FIG. 6, the peak height is higher at the peak portion than when the smoothing process is performed by fixing the smoothing width to 21 points by adjusting the smoothing width using the standard error. Therefore, the dent becomes large in the valley between the peaks. Therefore, by adjusting the smoothing width using the standard error, separation of adjacent peaks is improved as compared with the case where the smoothing width is fixed at 21 points.

  In the embodiment described above, the standard error SE is normalized to determine the normalized standard error SE ′ before the smoothing width is determined, and the smoothing width is determined based on the normalized standard error SE ′. However, the present invention is not limited to this, and a smoothing width table is prepared so that the smoothing width can be determined based on the standard error SE. The smoothing width may be determined by applying the standard error SE.

  Next, an example of a computer in which a smoothing program for executing the above-described smoothing method is introduced will be described with reference to FIG.

  An arithmetic processing unit 4 is electrically connected to the analyzer 2. The arithmetic processing device 4 is realized by, for example, a general-purpose personal computer (PC), but may be a computer dedicated to the analysis device 2. A detector signal acquired at a constant period in the analysis device 2 is input to the arithmetic processing device 4 as numerical data. The arithmetic processing unit 4 stores a smoothing program 6 for performing smoothing of numerical data output from the analysis unit 2.

  The smoothing program 6 includes a standard error calculation unit 8, a standard error normalization unit 10, a smoothing width determination unit 12, and a smoothing processing unit 14. The arithmetic processing unit 4 includes a smoothed width table holding unit 16 that holds a smoothed width table (for example, Table 2 or Table 3) created in advance. The smoothing width table holding unit 16 is realized by an area of the data storage device provided in the arithmetic processing device 4.

  The standard error calculation unit 8 is configured to calculate the numerical data SE of each data acquisition point or the standard error SE of the data based thereon using, for example, the above equation (1).

  The standard error normalization unit 10 is configured to normalize the standard error SE so that the standard error SE can be applied to the smoothing width table to obtain the normalized standard error SE '. The standard error normalization unit 10 is not an essential component, and is not necessary when the standard error SE itself is used to determine the smoothing width.

  The smoothing width determination unit 12 is configured to determine the smoothing width by applying the normalized standard error SE ′ or the standard error SE to the smoothing width table.

  The smoothing processing unit 14 uses the smoothing width determined by the smoothing width determining unit 12 and uses, for example, a smoothing processing method such as the Savitzky-Golay method to calculate numerical data at each data acquisition point or data based on the data. A smoothing process is performed.

2 Analyzing device 4 Arithmetic processing device 6 Smoothing program 8 Standard error calculation unit 10 Standard error normalization unit 12 Smoothing width determination unit 14 Smoothing processing unit 16 Smoothing width table holding unit

Claims (4)

Smoothing numerical data acquired at multiple data acquisition points or data based on it using numerical data of data acquisition points within the smoothing width including the data acquisition points from which each numerical data was acquired or data based on it A data smoothing method for
A standard error calculating step for calculating a standard error of the numerical data of each data acquisition point or data based thereon; and
After the standard error calculation step, the smoothing width of each data acquisition point is set so that the smoothing width becomes narrower as the data acquisition point has a larger standard error of numerical data or data based thereon. A smoothing width determining step for determining based on the standard error of the numerical data or data based thereon;
A smoothing step of performing a smoothing process of the numerical data of each data acquisition point or data based thereon using the numerical data of the data acquisition point within the smoothing width determined in the smoothing width determination step or data based thereon And a data smoothing method.   2. The smoothing width determination step according to claim 1, wherein the smoothing width of each data acquisition point is determined based on the standard error calculated in the standard error calculation step and a smoothing width table prepared in advance. Data smoothing method. A normalization step of normalizing the standard error calculated in the standard error calculation step by a predetermined calculation method after the standard error calculation step and before the smoothing width determination step;
The data according to claim 2, wherein in the smoothing width determination step, the smoothing width of each data acquisition point is determined based on the standard error normalized in the normalization step and a smoothing width table prepared in advance. Smoothing method.   A program configured to execute the data smoothing method according to any one of claims 1 to 3 by being executed by a computer.

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