JP2556768B2 - Multi-component analysis method in spectroscopic analysis - Google Patents

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method of irradiating a sample with light from a light source and analyzing the concentration of multiple components contained in the sample based on the absorption spectrum obtained at that time.

[0002]

2. Description of the Related Art For example, in a method for spectrally analyzing multiple components based on an infrared absorption spectrum, a method generally used in the past has been
It is performed by a linear algebraic method based on the Lambert-Beer law that the absorbance is proportional to the concentration of the measured component. This Lambert-Beer law can be expressed as follows. A (ν) = Cα (ν) (1) where C is the concentration of any absorber, α (ν) is the absorption spectrum of unit concentration at wave number ν, and A (ν) is the absorber of unknown concentration. FIG. 9 is an absorption spectrum at a wave number ν of, and schematically shows this relationship.

In the figure, a curve I shows an absorption spectrum α (ν) at a unit concentration, and a curve II shows an absorption spectrum at an unknown concentration. Then, when the absorptions of a plurality of components are superposed, the above formula (1) is represented by a simple linear combination of A (ν) = Σ _i C _i α _i (ν) (2). Here, C _i is the concentration for each component, and α _i (ν) is the absorption spectrum of the unit concentration for each component.

In the multi-component spectroscopic analysis using the infrared absorption spectrum which is generally performed, a reference spectrum α _i (ν) for each component is obtained in advance at the calibration stage, and the unknown mixture to be measured is measured. The concentration C _{i of} each component is estimated from the absorption spectrum A (ν). Usually, A ([nu) so is measured as a value corresponding to a continuous wave number points over 400 cm ^-1 from 4000 cm ^-1 in the infrared region,
The equation (2) is expressed by a simultaneous linear equation of the form A (ν _i ) = Σ _i C _i α _i (ν _i ) ... (3). Therefore, by carrying out the operation of this simultaneous linear equation using a matrix, the multi-component concentration is estimated.

FIG. 10 shows a typical superposition of absorption spectra of two components. In the figure, curves I and I
I is the absorption spectrum α _i of the unit concentration of each component gas
(Ν _i ) and α ₂ (ν _i ) are shown, and the curve III shows the linear combination of the spectra (formula (3) above).

[0006]

However, in the above-mentioned conventional method, when the number of kinds of components contained in the sample to be measured is large, the matrix used for the calculation becomes too large, and the computer used for the calculation is large. A large capacity memory is required. Further, when it becomes necessary to exchange the matrix used during the calculation, the calculation of all the components is interrupted, which causes a problem that the time is wasted.

In view of the above-mentioned conventional drawbacks, the present invention aims to provide a multi-component analysis method in spectroscopic analysis in which the matrix used for calculating the component concentration based on the absorption spectrum can be made small and the processing time can be greatly shortened. It is a thing.

[0008]

In order to achieve the above object, in the present invention, a sample is irradiated with light from a light source,
Included in the sample based on the absorption spectrum obtained at
A method of analyzing the concentration of multi-component, the multicomponent grouped into a plurality of component groups, apart from blocking Then Tomo component group the frequency area used for spectroscopic analysis of each component group
To each of multiple component groups in one spectrum.
Prepare the corresponding matrices and use each of these matrices
By calculating for each component group,
I try to quantify it .

[0009] In the present invention, the multi-component contained in the sample grouped into a plurality of component groups, apart from blocking Then Tomo component group the frequency area used for spectroscopic analysis of each component group
To each of multiple component groups in one spectrum.
Prepare the corresponding matrices and use each of these matrices
Since the calculation is performed for each component group, the matrix used for the concentration calculation becomes small and the calculation can be simplified. That
Then, even when the matrix is replaced during the arithmetic processing, only the matrix corresponding to the required component group needs to be replaced, so that the time waste associated with the matrix exchange can be reduced accordingly. Further, since the calculation can be omitted for the frequency region of the absorption spectrum which is unnecessary for the concentration calculation, the calculation time can be shortened accordingly.

[0010]

Embodiments of the present invention will be described below with reference to the drawings. FIG. 1 shows a schematic configuration of an FT-IR (Fourier transform infrared analyzer) 1 which is an example of an apparatus for carrying out a multi-component analysis method in a spectroscopic analysis according to the present invention. The FT-IR 1 is composed of a folding unit 2 and a data processing unit 3 that processes the interferogram output from the analysis unit 2.

The analysis unit 2 accommodates a light source 4 configured to emit a parallel infrared beam, an interference mechanism 8 including a beam splitter 5, a fixed mirror 6, and a movable mirror 7, a measurement sample, and the like, and causes interference. The cell 9 includes an infrared beam emitted from the light source 4 through the mechanism 8 and a detector 10 such as a semiconductor detector.

The data processing unit 3 includes, for example, an averaging processing unit 11 for averaging the interferobrams, a fast Fourier transform processing unit 12 for fast Fourier transforming the output data from the averaging processor 11, and the fast Fourier transform. It is composed of a spectrum calculation unit 13 and the like that performs spectrum calculation on the measurement target component based on the output data from the processing unit 12.

Although not shown, the FT-IR 1 is provided with a drive mechanism for driving the movable mirror 7 of the interference mechanism 8 in, for example, the XY directions, and the drive mechanism and the data processing section. A controller for controlling each of the three processing units 11 to 13 is provided.

In the FT-IR1 thus constructed,
The cell 9 contains the comparative sample and the measurement sample, and the interferograms of the comparative sample and the measurement sample are measured. When Fourier transform is performed on each of these interferograms to obtain the power spectrum, that is, the spectrum of the light transmitted through the cell 9, then the ratio of the power spectrum of the measurement sample to the power spectrum of the comparative sample is obtained. An absorption spectrum is obtained by converting to an absorbance scale.

Next, details of the multi-component analysis method of the present invention will be described. Now, assuming that the exhaust gas of a general gasoline engine automobile is used as a measurement sample and the concentration of each component thereof is quantified using an infrared absorption spectrum, here, each of these components is measured as shown in Table 1 below. Group into one component group A, B, C.

[0016]

[Table 1]

That is, the components of the exhaust gas are NO ₂ ,
_{SO 2, CH 4, NH 3} , CO 2, CO, H 2 O, N
O and other hydrocarbons such as C ₂ H ₂ , C ₂ H ₄ and C ₂ H ₆ (hydrocarbons), wherein the above hydrocarbon group is composed of one component group A and C.
O ₂ , CO, H ₂ O, and NO are different component groups B, NO ₂ , and S
O ₂ , CH ₄ , and NH ₃ are divided into three groups as another component group C.

As the wave number region of the infrared absorption spectrum, the component group A is 3200 cm ^{-1 to} 3000.
The limited range of cm ⁻¹ is 2400 c for the component group B.
The limited range of m ^-1 ~1800cm ^-1, for the component group C employing respectively limited to a range of ^{1500cm -1 ~1000cm} -1. These wave number regions are set with reference to the absorption spectra of the individual components included in each component group.

For each component group, as means for determining the concentration of each component contained in the component group in the exhaust gas,
For example, a conventional linear algebraic method or the like can be adopted. Here, a case will be described in which each of the above component groups is generalized as a group including three components of X, Y, and Z, and the concentrations of these three components are quantified by another method.

First, the concept of the sum of relative absorbances introduced in this method will be briefly described.
The spectrum output from the spectrometer is generally
Since noise is included due to various causes, the above equation (1) can be expressed as A (ν _i ) = Cα (ν _i ) + ε _i (4). Here, ε _i is noise included in the spectrum.

Then, at any two points in the spectrum,
Focusing on the difference, the above equation (4) is_p) -A (ν_b) = C [α (ν_p) -Α (ν_b)] + Ε_p−ε_b  It is expressed as (5), and the relative absorbance between such two points is also
It is shown to obey Invert Beer's law. here,
p and b correspond to the peak and base of the spectrum, respectively.
Is a subscript indicating the wave number point.

Generally, the spectrum of a substance, particularly the spectrum of a gas, contains a large number of peaks, and a large number of pairs of the wave point ν _{p of the} peak and the wave number ν _b of the base can be selected.

FIG. 2 shows an example of a typical gas absorption spectrum and corresponding relative absorbances L ₁ , L ₂ and L ₃ . The respective relative absorbances L ₁ , L ₂ and L ₃ correspond to the values of the equation (5).

Taking the sum of these values gives Σ_k[A (ν_p) -A (ν_b)]_k  = CΣ_k[Α (ν_p) -Α (ν_b)]_k+ Σ_k(Ε_p−ε_b)_k  (6), and this equation (6) maintains Lambert-Beer's law.
are doing. Then, from this equation (6), the second term on the right side
Averages the random noise latent in the spectrum
And like the drift of the baseline
It turns out that the major disturbance has been cancelled.

Here, the value calculated by the above equation (6) is
MAS (Multiple Absorption S)
um) value. That is, MAS = Z _k [A (ν _p ) −A (ν _b )] _k (7) Then, in particular the MAS value determined for the reference spectrum of known concentration in a single component, the MAS _i to component i.

FIG. 3 shows an example of designation of wave number points for three gas species included in the above-mentioned generalized component group. In the figure, curves 1, II, and III are gas X,
The reference spectra of Y and Z are shown. And gas X
Φ _X : (X _p ,, X _b ), the set of wave points for gas Y Φ _Y : (Y _p , Y _b ) _k , and the set of wave points Φ _Z for gas _Z : (Z _p , Z _b ) _k are designated respectively. When designating these peak-base pairs, it is preferable to obtain a relative absorbance as large as possible and not to be influenced by the absorption of each other.

Here, by generalizing the story, the set of the above-mentioned wave point designation values for m components is expressed by Φ _i (i = 1 to 1).
m), an operation for calculating the set of peak-base pairs of the component i for one absorption spectrum as in the above equation (6) is defined as the following equation. Σ _k [A (ν _p ) −A (ν _b )] = A ◎ Φ _i (8) Here, ⊚ is a new operator, and expression (8) gives the MAS value.

Therefore, MAS _i = A ◎ Φ _i (9), and m MAS _i are calculated for m Φ _i . If MAS _i , which is a set of m numbers, is Ψ, this can be thought of as a spectrum having m elements. Ψ = (MAS _i : i = 1 to m) (10)

In this new spectral region (component spectral region), the horizontal axis represents gas species i, and the vertical axis represents the sum M of relative absorbances.
It can be displayed graphically as AS _i . Therefore, the equation (9) can be considered as the spectrum A converted into the component spectrum Ψ using the set Φ.
This will be described below by applying it to the component group generalized above.

FIG. 4 shows an absorption spectrum of a mixture of the three kinds of gases X, Y and Z shown in FIG. 3 at arbitrary concentrations, that is, an absorption spectrum of the above generalized component group as a whole. FIG. 4 shows the wave number specified values of the peak base pairs of the three gases specified in FIG.
Applied to the absorption spectrum of X, as shown in FIG.
The sum of the relative absorbances represented by Y and Z is calculated.
Then, as shown in FIG. 5, the sum of these relative absorbances is plotted in a region in which the horizontal axis represents the gas species and the vertical axis represents the sum of relative absorbances.

In the component spectrum thus obtained, the influence of noise is largely eliminated as described above, and the influence of interference between spectra between gas species is suppressed. As shown in FIGS. 4 and 5, if the components can be converted without interference, the sum of the relative absorptivities of the respective components in the component spectral region is proportional to the respective component concentrations. Obtainable.

However, in the actual gas absorption spectrum,
As shown in FIGS. 4 and 5, it is rare that the wave number point can be designated without interference, and it is common that some interference remains in the converted component spectrum region. Therefore,
In the quantitative analysis using the component spectrum region, it is necessary to correct the above-mentioned slightly remaining interference, and the following processing is performed in the calibration step for creating a matrix (calibration matrix) used for interference correction, that is, for the interference correction. It is divided into a step of preparing data and an estimation step of calculating an unknown concentration using the data.

At the calibration stage, the calibration matrix is obtained as follows. If there is a reference spectrum α _i (i = 1 to m) of unit concentration for m components, generalization is performed, and the set Φ _i of the wave point specified values described above is applied to these reference spectra, and by applying the transformation shown by 9), component spectra corresponding to α _i Ψ _{i (i}
= 1 to m) can be obtained. More specifically, it can be obtained by obtaining the sum of the relative absorbances when a plurality of gases are individually used as samples.

FIGS. 6A, 6B, and 6C show reference component spectra for the three gas species X, Y, and Z contained in the component group generalized above. The calibration matrix is

[0035]

[Equation 1]

It becomes On the other hand, the component spectrum of the component group can be obtained as shown in FIG. 7 from the absorption spectrum obtained by spectrally analyzing the sample to be measured in the wave number region assigned to the component group. The component spectrum Ψ in this case
_u is

[0037]

[Equation 2]

## EQU4 ## Generally, m gas components (i = 1
˜m), ψ _u is represented by a linear combination of ψ _i , where C _i (i = 1 to m) is the unknown concentration of each gas component. That is, Ψ _u = C ₁ Ψ ₁ + C ₂ Ψ ₂ + ... + C _m Ψ _m (11) always holds, and if this is rewritten using a matrix, Ψ _u = CΩ ...... (12) It can be expressed as.

Here, C is a vector of unknown concentrations, and Ω is a matrix having Ψ _i as a row, which is called a calibration matrix in the component spectral region. Therefore,
If the unknown concentrations of the three gas species X, Y, Z of the above-mentioned component group are C _X , C _Y , C _Z ,

[0040]

(Equation 3)

It becomes At the calibration stage, it is necessary to accurately determine the Ω. Also, as already mentioned, Ψ
_{Since i} is a vector with high linear independence, that is, a vector with little interference, Ω is a matrix that can obtain a stable inverse matrix.

Next, in the estimation stage, the above equation (12) is changed to C
The unknown concentration can be estimated by solving for C = Ψ _u Ω ⁻¹ . And also regarding the above equation (13),

[0043]

[Equation 4]

By the above, C _X , C _Y , and C _Z can be obtained respectively. The inverse matrix calculated here is Ω
Since the linear independence of is high, we can obtain a stable solution,
Therefore, the error due to the numerical calculation of the estimated concentration is extremely small.

The above method is applied to the above-mentioned component groups A, B,
By applying each C, where components contained in each component group, so that you can quantify the concentration for that is all components in the measurement sample.

In this case, each component group is divided into pairs.
Since the arithmetic processing described above is performed using the corresponding matrix ,
As the number of components included in each component group becomes smaller, the matrix used in the calculation becomes smaller and the calculation process can be simplified. Moreover, since the wave number region used for each component group is not the entire region of the infrared region but a limited range that is blocked for each component group is assigned, the calculation process only needs to be performed for that limited range. This also shortens the time required for arithmetic processing.

In addition, for example, a situation in which the concentration of the component contained in one component group is higher than that initially predicted, and the absorption spectrum at the selected wave number point is not completely within the measurement range is a calculation process. If it occurs on the way, another wave number point must be specified so that it falls within the measurement range and the arithmetic processing is performed. In this case, the matrix also needs to be replaced with the one corresponding to the new wave number point, so that some time is required for the replacement process.

However, here, since the spectral analysis is performed by dividing into a plurality of component groups, the recalculation is limited to only a specific component group, and the overall processing efficiency is greatly affected. It can be done without giving.

Next, as another embodiment, the case of quantifying the components of the exhaust gas of a methanol-fueled automobile (hereinafter simply referred to as exhaust gas) will be described. FIG. 8 shows the FT shown in FIG.
The absorption spectrum obtained by -IR1 is shown. In this figure, I is a reference spectrum with methanol having a concentration of 103.7 ppm, and II is a concentration of 26.4 ppm.
Of the reference spectrum of formaldehyde only, II
I indicates the absorption spectrum of the exhaust gas. In this figure, the vertical axis indicating the absorbance uses an arbitrary scale.

As is apparent from FIG. 8, in the case of this exhaust gas, the absorption wave number band, that is, the wave number region of the absorption spectrum is 28
In the range of 50cm ^-1 ~2700cm ^-1, the absorption spectrum of the gas III methanol reference spectrum I
And the reference spectrum II of formaldehyde are superposed, and it can be seen that there is no absorption by other gas components contained in the same exhaust gas.

Therefore, paying attention to this point, in the quantification of the components of the exhaust gas, two components of methanol and formaldehyde are distinguished as one component group from the other components, and the spectroscopic analysis of this component group is 2850 cm ^−1. ~ 2700c
This is limited to the wave number region of m ⁻¹ . For the specific calculation processing, the method shown in the previous embodiment may be used, or it is estimated by a linear algebraic method such as the least squares method, and the ratio thereof is actually calculated by using the density data of the reference spectrum. You may convert into a density value.

It should be noted that, with respect to the remaining component groups distinguished from the above-mentioned two components, their respective concentrations can be similarly quantified, but in the exhaust gas of a methanol-fueled automobile, in practice, the above-mentioned two components of methanol and formaldehyde are used. Is especially important from the viewpoint of toxicity check,
Quantitation of the concentrations of other components is not important. Therefore, the exhaust gas quantitative processing is substantially completed only by the quantitative determination of the two components. Therefore, as in the conventional case, for example, the entire absorption wave band (4000 cm ⁻¹ to 40) of the absorption spectrum is
Since it is not necessary to measure over 0 cm ⁻¹ , the processing time can be shortened.

[0053]

Industrial Applicability The present invention has the above-mentioned constitution, and in a method of irradiating a sample with light from a light source and analyzing the concentration of multi-components contained in the sample based on the absorption spectrum obtained at that time, The multi-component is grouped into a plurality of component groups, and the frequency domain used for the spectral analysis of each component group is divided into component groups and one spectrum
Prepare matrices corresponding to multiple component groups in
And calculate each component group using these matrices.
To quantify each component.
ing. That is, in the present invention, one spectrum is
Prepare multiple matrices and use these matrices to create each matrix.
Since the concentration is calculated for each sub-group, the matrix used for the concentration calculation is small, and the calculation can be simplified. That
Then , even when the matrices are replaced in the middle of the arithmetic processing, only the matrix corresponding to the required component group needs to be replaced, so that the time waste associated with the matrix exchange can be reduced accordingly. In addition , regarding the frequency region of the absorption spectrum that is unnecessary for concentration calculation,
Since the calculation can be omitted, the calculation time can be shortened accordingly.

[Brief description of drawings]

1 is a diagram schematically showing an example of an apparatus for carrying out the method of the present invention.

FIG. 2 is a diagram of a typical gas absorption spectrum and a relative absorbance corresponding thereto, which are shown for explaining a calculation method used in one embodiment of the method of the present invention.

FIG. 3 is a diagram showing an example of designating wave number points for gas species by generalizing the component group in the embodiment.

FIG. 4 is a diagram showing an absorption spectrum of a generalized component group in the example.

FIG. 5 is a diagram showing an example of a component spectrum calculated from an absorption spectrum of a generalized component group in the example.

FIG. 6 is a diagram showing reference component spectra corresponding to a generalized component group in the example.

FIG. 7 is a diagram showing a component spectrum calculated from an absorption spectrum of a measurement sample in the example.

FIG. 8 is a diagram showing an absorption spectrum and a reference spectrum of one component group in another example of the method of the present invention.

FIG. 9 is a diagram showing a general absorption spectrum for explaining the problems of the conventional technique.

FIG. 10 is a diagram showing a schematic superposition of spectra of two components.

[Explanation of symbols]

 1 FT-IR 2 analysis part 3 data processing part 4 light source 9 cells

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Claims (2)

(57) [Claims] 1. A method of irradiating a sample with light from a light source and analyzing the concentration of multi-components contained in the sample based on the absorption spectrum obtained at that time, wherein the multi-components are grouped into a plurality of component groups. And block the frequency domain used for spectral analysis of each component group by component group ,
Corresponds to multiple component groups in one spectrum
Matrix and prepare each matrix using
By calculating for each subgroup, the individual components can be determined.
A multi-component analysis method in spectroscopic analysis characterized by quantification . 2. The sample is exhaust gas from a methanol fueled vehicle, and formaldehyde and methanol in the exhaust gas are classified as one component group from other components, and the concentration of each component of this component group is from 2800 cm ^−1. 2700 cm
The multi-component analysis method in the spectroscopic analysis according to claim 1, wherein the spectroscopic analysis is performed in the absorption wave number band of ^-1 .