JP7401768B2 - Gas analysis method and gas analysis device - Google Patents

Description

The present invention relates to a gas analysis method and a gas analysis apparatus for analyzing the spatial distribution of the temperature and concentration of a gas to be measured in a measurement chamber containing the gas to be measured in the range of 500° C. to 2000° C.

In combustion heating furnaces that are frequently used in the steel manufacturing process, measurement technology that quantitatively monitors the temperature distribution and material concentration distribution inside the furnace is an important technology that is directly linked to the optimal operation of heating furnaces that consume large amounts of fuel. As one promising technology for realizing the measurement of temperature distribution and concentration distribution, for example, CT-TDLAS (Computed Tomographic and Tunable Diode Laser Absorption Spectroscopy) is proposed in Non-Patent Document 1.

The advantage of CT-TDLAS is that it can measure the state inside the heating furnace without contact. In other words, the laser beam that enters the furnace from outside the furnace is measured by the light receiving section outside the furnace on the opposite side, and the spectrum is analyzed to obtain temperature information and concentration information as the optical path integral value of the laser beam. (TDLAS technology). Furthermore, by configuring the path of this laser beam in a grid pattern, it is possible to obtain temperature distribution and concentration distribution in a plane or space within the furnace (CT technology).

Takahiro Kamimoto, Yoshihiro Deguchi et al. 56th Japan Heat Transfer Symposium Proceedings (2019) G112-G125

However, the CT image reconstruction algorithm disclosed in Non-Patent Document 1 has the following problems, resulting in unstable calculations and excessive calculation costs.

First, in the CT image reconstruction algorithm disclosed in Non-Patent Document 1, the temperature distribution T (x, y) and the concentration distribution n (x, y) on the measurement surface are approximated by bim-order polynomials, and each constant The coefficients are determined by an optimization calculation method, but the problem is that the order of m is as high as 14th order. In other words, the number of constant coefficients to be optimized is 2 x (14 + 1) ² = 450 variables, so if the initial search value of the optimization calculation is not set appropriately, the global optimal solution may not be reached or it may take a long time until the global optimal solution is reached. The problem is that it takes a lot of time. In addition, approximation using high-order polynomials also presents a mathematical problem in that unstable numerical oscillations, generally referred to as the Runge phenomenon, occur. In order to suppress this numerical oscillation, it is practically desirable to use an order of about m≦6, but this order cannot cope with cases where the temperature distribution has multimodality. Furthermore, in a high-order polynomial, the number of digits of each constant coefficient is different, making calculations unstable. Furthermore, since the constant coefficients of a high-order polynomial have no physical meaning, if the calculation becomes unstable, it is difficult to identify the variable that causes the instability.

Second, in the CT image reconstruction algorithm disclosed in Non-Patent Document 1, in order to shorten the time to arrive at the above-mentioned global optimal solution, an initial value database is constructed, and the optimal search initial value is determined from a linear combination of the databases. However, there is a problem with setting the initial value for this search. In other words, the initial search values are set appropriately by, for example, CFD (Computational Fluid Dynamics) calculations, but this CFD calculation itself requires calculation costs, and the conditions for CFD calculations also need to be appropriately set manually. There is.

The present invention has been made in view of the above circumstances, and aims to realize stable calculations and reduce calculation costs in a CT image reconstruction algorithm for CT-TDLAS.

In order to achieve the above object, the inventors of the present invention conducted extensive studies and came up with a CT image reconstruction calculation algorithm that simultaneously solves the first problem and the second problem. In other words, in the algorithm disclosed in Non-Patent Document 1, the temperature distribution T (x, y) and the concentration distribution n (x, y) on the measurement surface are approximated by a high-order polynomial, but they are approximated by a discrete grid. Assuming a temperature distribution T (x, y) and a concentration distribution n (x, y), interlattice intervals are interpolated using a polynomial interpolation formula of order three or less. This ensures continuity and first-order differential continuity at the lattice boundaries, creating a continuously smooth temperature distribution T (x, y) and concentration distribution n (x, y) with low order It can be obtained as a polynomial.

Further, for the temperature distribution T(x, y) and concentration distribution n(x, y) assumed to be in the form of a discrete grid, the values closest to the measured values can be selected by appropriate optimization calculations. Furthermore, by gradually narrowing the assumed lattice spacing, it is possible to stably improve the accuracy of optimization calculations. With this procedure, it is possible to reach the optimal solution stably and quickly without starting the search sufficiently close to the optimal solution.

The present invention has been made based on this knowledge, and is a gas analyzer for analyzing the spatial distribution of the temperature and concentration of the gas to be measured in a measurement chamber containing the gas to be measured in the range of 500°C to 2000°C. The analysis method comprises: irradiating a laser beam from a laser incident part toward a laser receiving part, passing the laser light into the gas to be measured, and measuring the intensity of the laser light received by the laser receiving part. and a calculation step of calculating the spatial distribution of the temperature and concentration of the gas to be measured based on the measured value of the laser light intensity in the laser light receiving part, A plurality of pairs of the laser light receiving sections are provided, and the calculation step includes a first step of discretely estimating the estimated values of the temperature and concentration of the gas to be measured within the internal space of the measurement chamber; a second step of performing spatial interpolation of the estimated value discretely estimated in the step using a polynomial interpolation formula of order three or less; a laser light intensity calculated from the estimated value estimated in the first step; and the measurement. a third step of performing an iterative optimization calculation to correct the estimated value so as to minimize the error with the measured value of the laser light intensity measured in the third step; The present invention is characterized by comprising a fourth step of increasing the number of points in the space of estimated values stepwise to calculate the spatial distribution of the temperature and concentration of the gas to be measured.

In the gas analysis method, eight or more pairs of the laser entrance section and the laser reception section are provided, and the laser light path between the laser entrance section and the laser reception section is two-dimensional within the gas to be measured. It may be configured to have a mesh shape.

In the gas analysis method, in the second step, a bicubic convolutional interpolation method may be used as the polynomial interpolation formula of order three or less.

In the gas analysis method, a least squares method may be used as the iterative optimization procedure in the third step.

In the gas analysis method, in the fourth step, the grid interval in the estimated value space may be successively divided into two as a step of increasing the number of points in the estimated value space in stages. .

The present invention according to another aspect is a gas analyzer for analyzing the spatial distribution of the temperature and concentration of the gas to be measured in a measurement chamber containing the gas to be measured in the range of 500° C. to 2000° C. A laser light entrance part that enters the laser light into the gas to be measured, a laser light receiving part that receives the laser light that has passed through the gas to be measured, and based on the measured value of the laser light intensity in the laser light receiving part, a calculation unit that calculates the spatial distribution of the temperature and concentration of the gas to be measured; a plurality of pairs of the laser light input unit and the laser reception unit are provided; A first step of discretely estimating estimated values of temperature and concentration within the internal space of the measurement chamber, and spatial interpolation of the estimated values discretely estimated in the first step using a polynomial interpolation formula of order three or less. The second step performed in the second step and the laser light intensity calculated from the estimated value estimated in the first step and the measured value of the laser light intensity at the laser receiver are minimized. A third step of performing an iterative optimization calculation to correct the estimated value, and stepwise increasing the number of points in the space of the estimated value corrected in the third step, and adjusting the temperature and concentration of the measured gas. A fourth step of calculating the spatial distribution is performed.

In the gas analyzer, eight or more pairs of the laser entrance section and the laser reception section are provided, and the laser light path between the laser entrance section and the laser reception section is two-dimensional within the gas to be measured. It may be configured to have a mesh shape.

In the gas analyzer, the calculation unit may use a bicubic convolution interpolation method as the polynomial interpolation formula of order three or less in the second step.

In the gas analyzer, the calculation unit may use a least squares method as the iterative optimization procedure in the third step.

In the gas analyzer, in the fourth step, the calculation unit sequentially increases the grid spacing in the estimated value space by 2 as a step of increasing the number of points in the estimated value space in stages. May be divided.

According to the present invention, in the CT image reconstruction algorithm of CT-TDLAS, stable calculation can be realized and the calculation cost can be reduced.

FIG. 1 is an explanatory diagram schematically showing the configuration of a gas analyzer according to the present embodiment. It is an explanatory diagram showing temperature distribution T (x, y) and concentration distribution n (x, y). FIG. 3 is an explanatory diagram showing how the number of points in the space of estimated values of temperature distribution T(x, y) and concentration distribution n(x, y) is increased in stages. It is an explanatory view showing an original image in an example. FIG. 3 is an explanatory diagram showing the transition of the sum of mean square errors of absorbance in Examples. FIG. 2 is an explanatory diagram showing an image reconstructed using a CT image reconstruction calculation algorithm in an example.

Embodiments of the present invention will be described below with reference to the drawings. Note that in this specification and the drawings, elements having substantially the same functional configuration are designated by the same reference numerals and redundant explanation will be omitted.

<Gas analyzer>
First, the configuration of the gas analyzer according to this embodiment will be explained. FIG. 1 is an explanatory diagram showing an outline of the configuration of a gas analyzer.

As shown in FIG. 1, the gas analyzer 10 is a device that measures and analyzes the spatial distribution of temperature and concentration of a gas to be measured contained within a measurement chamber 20. The measurement chamber 20 is, for example, a chamber in a hot rolling heating furnace, and the gas to be measured therein is a gas in the range of 500°C to 2000°C. This range of 500°C to 2000°C almost coincides with the measurement limit in TDLAS.

The gas analyzer 10 has a plurality of laser light receiving sections 11 and a plurality of laser light receiving sections 12. The laser light entrance unit 11 irradiates the inside of the measurement chamber 20 with laser light, and enters the laser light into the gas to be measured. The laser light receiving section 12 receives the laser light irradiated from the laser light receiving section 11 and passed through the gas to be measured.

The laser light incident section 11 and the laser light receiving section 12 are provided in a one-to-one pair with the measurement chamber 20 in between. A plurality of pairs, 16 in this embodiment, of the laser light incident section 11 and the laser light receiving section 12 are provided. In the following description, these 16 laser light incident sections 11 and laser light receiving sections 12 may be referred to as laser light incident sections 11a to 11p and laser light receiving sections 12a to 12p, respectively. Each pair of laser light incident portions 11a to 11h and laser light receiving portions 12a to 12h are arranged to face each other in the X direction with the measurement chamber 20 in between. Each pair of laser light incident sections 11i to 11p and laser light receiving sections 12i to 12p are arranged to face each other in the Y direction with the measurement chamber 20 in between. The laser beam paths of the laser light incident section 11 and the laser light receiving section 12 are configured to form a two-dimensional mesh within the gas to be measured in the measurement chamber 20.

Note that the number of pairs of the laser light incident section 11 and the laser light receiving section 12 is not limited to this embodiment, but from the viewpoint of improving the accuracy of calculations described later, it is preferably eight or more, for example. Further, in the present embodiment, the laser light incident section 11 and the laser light receiving section 12 are configured so that the laser light path forms a two-dimensional mesh within the gas to be measured, but the invention is not limited to this. For example, the laser light incident section 11 and the laser light receiving section 12 may be configured such that their laser light paths intersect at 45 degrees.

The gas analyzer 10 determines the concentration of the gas to be measured and the space between the temperature and the concentration of the gas to be measured based on the measured value of the intensity of the laser light received by the laser light receiving unit 12 (hereinafter referred to as "laser light intensity"). It has a calculation unit 13 that calculates the inner distribution. The calculation unit 13 is, for example, a computer equipped with a CPU, a memory, etc., and has a program storage unit (not shown). The program storage section stores various programs for performing gas analysis. Note that communication between the laser light receiving section 12 and the calculation section 13 is not particularly limited, and may be configured, for example, by the Internet, a wired LAN, a wireless LAN, or the like.

<Gas analysis method>
Next, a method for calculating (analyzing) the spatial distribution of the temperature and concentration of the gas to be measured inside the measurement chamber 20 using the gas analyzer 10 of the above embodiment, that is, a CT image reconstruction calculation algorithm will be described. explain.

[Measurement process]
First, a laser beam is irradiated from the laser light receiving part 11 toward the laser receiving part 12, and the laser light is passed through the gas to be measured inside the measurement chamber 20, and the intensity of the laser light received by the laser receiving part 12 is measured. Measure. The measurement results at the laser light receiving sections 12a to 12p are output to the calculation section 13.

[Calculation process]
Next, a process of calculating the spatial distribution of the temperature and concentration of the gas to be measured in the calculation unit 13 will be explained. This calculation process is divided into the following first to fourth steps.

(1st step)
In the first step, estimated values of the temperature and concentration of the gas to be measured are discretely estimated within the internal space of the measurement chamber 20 . As shown in FIG. 1, the laser light path of the laser light incident part 11 and the laser light receiving part 12 forms a two-dimensional mesh within the gas to be measured. In the first step, the temperature distribution T(x, y) and concentration distribution n(x, y) are estimated in a discrete grid on the measurement surface where the laser beam path is expressed as a two-dimensional mesh as shown in Figure 2. (corresponds to the white circle in Figure 2).

(Second process)
In the second step, the lattices of the estimated values discretely estimated in the first step are interpolated using a bicubic convolution interpolation method (BCI method). Specifically, the estimated value is interpolated using the following equation (1). As shown in Figure 2, the value of each neighboring point is interpolated using a cubic formula based on the distance from the target point (corresponding to the black circle in Figure 2) to the neighboring 4 x 4 = 16 points (corresponding to the white circle in Figure 2). The value of the target point is calculated by:

By interpolating between the grids of the temperature distribution T (x, y) and the concentration distribution n (x, y) using the bicubic convolution interpolation method, continuity at the grid boundaries (block boundaries) and first-order differentiation can be achieved. Continuity is guaranteed, and a continuously smooth temperature distribution T(x, y) and concentration distribution n(x, y) can be obtained using low-order polynomials. Furthermore, since it is a low-order polynomial, numerical oscillations such as the Runge phenomenon can be suppressed, and calculations can be performed with high accuracy and stability. Regarding the effects of using such a bicubic convolutional interpolation method, see, for example, "A Study on Cubic Convolutional Interpolation" by Hiromi Ueda, IEICE Technical Report Vol. 113, No. 114, (2013), pp. 7-14. It has also been reported.

In addition, when using the bicubic convolution interpolation method, there are the following advantages over the algorithm disclosed in Non-patent Document 1. Namely, in the algorithm disclosed in Non-Patent Document 1, the optimization calculation target are constant coefficients of a high-order polynomial, whereas in the bicubic convolution interpolation method, physical coefficients such as temperature distribution T and concentration distribution n are directly targeted for optimization. becomes easier. In addition, in high-order polynomials, the number of digits of each constant coefficient differs greatly, but with the bicubic convolution interpolation method, the number of digits of the coefficients to be optimized can be made the same as shown in equation (1) above, making calculations easier. It can be stabilized. Furthermore, in a high-order polynomial, the modification of one constant coefficient affects the distribution state of the entire target space, but in the bicubic convolution method, the influence of modification of one assumed value is limited only to the local space around it. , the optimization calculation can proceed more stably.

Note that in this embodiment, the bicubic convolution interpolation method is used as spatial interpolation of estimated values, but the interpolation method is not limited to this. For example, it is preferable to interpolate the estimated value using a polynomial interpolation formula of order three or less. For example, cubic spline interpolation (bicubic spline interpolation) or NURBS (Non-Uniform Rational B-Spline) may be used. When these methods are used, even second-order differential continuity is guaranteed, but the computational load increases. Alternatively, for example, bilinear interpolation may be used. In such a case, the value of the target point is calculated by linearly interpolating the value of each neighboring point from the distance to 2×2=4 points in the vicinity of the target point. When this bilinear interpolation is used, continuity at the grid boundaries is guaranteed and the calculation load is reduced, but there is no first-order differential continuity at the grid boundaries and the interpolation accuracy is poor. Therefore, in comprehensive consideration of calculation load and interpolation accuracy, it is preferable to use the bicubic convolutional interpolation method for spatial interpolation of estimated values.

(3rd step)
In the third step, the estimated value is corrected so as to minimize the error between the laser light intensity calculated from the estimated value estimated in the first step and the measured value of the laser light intensity measured in the measurement step. Perform iterative optimization calculations. Then, for the estimated values of the temperature distribution T(x, y) and the concentration distribution n(x, y) estimated in the form of a discrete grid, the values closest to the measured values can be selected.

For example, the method of least squares is used for the iterative optimization calculation described above. In this embodiment, a simple nonlinear simplex method such as the Nelder-Mead method is used. Note that the optimization calculation method is not limited to this. For example, the conjugate gradient method, SA method (Simulated Annealing), GA method (Genetic Algorithm), SB method (Simulated Bifurcation), etc. may also be used.

(4th step)
In the fourth step, the number of points in the space of the estimated values corrected in the third step is increased in stages, and the lattice spacing of the estimated values is gradually narrowed. For example, as shown in FIG. 3, the grid spacing in the estimated value space is narrowed by 1/2. Thereby, the spatial distribution of the temperature and concentration of the gas to be measured can be calculated.

Note that the sequential increase in the number density in the estimated value space is not limited to this embodiment, and the grid interval may be divided into three or five, for example. However, if the lattice spacing of estimated values is successively divided into two as in this embodiment, calculation efficiency is improved.

Here, in the algorithm disclosed in Non-Patent Document 1, an algorithm is adopted in which an initial value database is constructed and an optimal search initial value is selected from a linear combination of the database, but since this search initial value is set by CFD calculation, , calculation costs are high, and calculation work must be done manually. On the other hand, in the fourth step of the present embodiment, by increasing the number of region divisions in half, it is possible to stably improve the accuracy of the optimization calculation. In addition, since the optimal solution can be reached stably and quickly without starting the search sufficiently close to the optimal solution, the above-mentioned initial value database is no longer required, realizing stable calculations and reducing calculation costs. be able to.

According to the above embodiment, in the second step, the temperature distribution T(x, y) and the concentration distribution n(x, y) on the measurement plane are approximated by a bim-order polynomial (m≒14) in the conventional method. The mathematical instability of high-order polynomials can be resolved by approximating this using bicubic convolution interpolation. Furthermore, in the fourth step, the calculation cost for setting the initial value can be reduced by gradually narrowing the interpolation division width. Therefore, in the CT image reconstruction algorithm of CT-TDLAS, high-speed and stable calculation can be realized, and the calculation cost can be reduced.

Although the embodiments of the present invention have been described above, the present invention is not limited to such examples. It is clear that those skilled in the art can come up with various changes or modifications within the scope of the technical idea described in the claims, and these naturally fall within the technical scope of the present invention. It is understood that it belongs to

In order to verify the effect (effectiveness) of the present invention, numerical verification was performed as follows.

First, as sample data, an absorbance distribution having three peaks in a rectangular plane as shown in FIG. 4 is assumed. The height and spread of each peak 1 to 3 are given as continuous values by a modified Gaussian function shown in equation (2) below. Table 1 shows the coefficients of each peak 1 to 3 in formula (2).

Next, assume that there are eight laser beam paths in the vertical direction and eight in the horizontal direction within the rectangular plane shown in FIG. 4, and the path average absorbance (path integrated absorbance) in each laser beam path is expressed by the following formula (3). Calculated using the theoretical formula for the TDLAS signal. Table 2 shows a list of the coordinates of the end points of each laser beam path and the calculated path average absorbance.

Then, from the simulated CT data shown in Table 2, the original image shown in FIG. 4 was reconstructed by the trial calculation means described in FIG. 3 and below.

First, a rectangular plane is divided into 2×2 blocks, and the absorbance at the apex of each small rectangle is assumed. That is, a total of nine hypothetical values (estimated values in the above embodiment) are generated at this stage. Further, the absorbance distribution within the rectangle is calculated by the bicubic convolution interpolation method shown in the above equation (1).

Next, the path average absorbance on the laser beam path is calculated based on the assumed absorbance. The error between this value and the sample data in Table 2 is compared, and if the error is large, the assumed value is corrected. Here, the sum of mean square errors is used as the error. In addition, as a method for correcting assumed values, a nonlinear simplex method such as the Nelder-Mead method was used in this example, but there are also other methods such as the conjugate gradient method, SA method, GA method, SB method, etc. may also be used.

If the error is small, the number of divisions of the rectangular plane is doubled, the absorbance at the apex of the newly generated small rectangle is added to the assumed value group, and the error comparison with the sample data and correction of the assumed value are repeated.

The above-described division of the rectangular plane and modification of the assumed absorbance value are repeated, and the calculation is completed when the rectangular division width becomes approximately half the distance between the laser beam paths.

FIG. 5 shows the transition of the sum of mean square errors in the above-mentioned iterative calculation. The horizontal axis of FIG. 5 shows the steps of iterative calculation (one calculation of the iterative calculation is one step), and the vertical axis shows the sum of mean square errors. Referring to FIG. 5, it is shown that the sum of squared errors becomes smaller as the calculation progresses.

Further, FIG. 6 shows an image reconstructed from the data at the final stage of the iterative calculation. It is shown that an absorbance distribution similar to the original image in FIG. 4 can be reconstructed. From this absorbance distribution, the concentration and temperature of the gas can be estimated using a model equation depending on the gas component and laser wavelength.

Table 3 summarizes the differences between the present invention and the conventional CT image reconstruction algorithm (CT-TDLAS) disclosed in Non-Patent Document 1. The conventional method required calculation time of 1 hour if the initial values were assumed, and about 1 week due to manual trials if no initial values were assumed, but the CT image reconstruction calculation algorithm of the present invention According to the method, the calculation can be completed in one second without assuming any initial values. In addition, when assuming an initial value in the conventional method, it usually takes about one week because it requires work to prepare calculation conditions in CFD calculation and time for CFD calculation, whereas in the present invention, setting of initial value is not necessary. From the above, it is shown that the CT image reconstruction calculation algorithm of the present invention significantly improves the calculation cost.

Further, while the distribution function of the conventional method is a bihigh-order polynomial, the distribution function of the present invention is a bicubic convolutional interpolation. The optimization variables of the conventional method are constant coefficients of a polynomial, whereas the optimization variables of the present invention are physical quantities such as temperature and concentration. Therefore, according to the CT image reconstruction calculation algorithm of the present invention, data visibility is good and data analysis becomes easy.

The present invention is useful when reconstructing CT images of CT-TDLAS.

10 Gas analyzer 11 (11a to 11p) Laser light incident section 12 (12a to 12p) Laser light receiving section 13 Calculation section 20 Measurement chamber

Claims (10)

A gas analysis method for analyzing the spatial distribution of the temperature and concentration of the gas to be measured in a measurement chamber containing the gas to be measured in the range of 500° C. to 2000° C.,
a measuring step of irradiating a laser beam from a laser light incident part toward a laser light receiving part, passing the laser light into the gas to be measured, and measuring the intensity of the laser light received by the laser light receiving part;
a calculation step of calculating the spatial distribution of the temperature and concentration of the gas to be measured based on the measured value of the laser light intensity in the laser light receiving section,
A plurality of pairs of the laser light incident part and the laser light receiving part are provided,
The calculation step is
A first step of discretely estimating the temperature and concentration of the gas to be measured within the internal space of the measurement chamber;
a second step of spatially interpolating the estimated values discretely estimated in the first step using a polynomial interpolation formula of order three or less;
Correcting the estimated value so as to minimize the error between the laser light intensity calculated from the estimated value estimated in the first step and the measured value of the laser light intensity measured in the measurement step. A third step of performing iterative optimization calculations;
A fourth step of calculating the spatial distribution of the temperature and concentration of the measured gas by increasing stepwise the number of points in the space of the estimated value corrected in the third step. , gas analysis methods. Eight or more pairs of the laser light incident part and the laser light receiving part are provided,
2. The gas analysis method according to claim 1, wherein the laser light path between the laser light incident part and the laser light receiving part is configured to form a two-dimensional mesh within the gas to be measured. 3. The gas analysis method according to claim 1, wherein in the second step, a bicubic convolutional interpolation method is used as the polynomial interpolation formula of order three or less. The gas analysis method according to any one of claims 1 to 3, characterized in that in the third step, a least squares method is used as the iterative optimization procedure. In the fourth step, as a step of increasing the number of points in the estimated value space in stages, the grid interval in the estimated value space is successively divided into two. The gas analysis method according to any one of Items 1 to 4. A gas analyzer for analyzing the spatial distribution of the temperature and concentration of the gas to be measured in a measurement chamber containing the gas to be measured in the range of 500° C. to 2000° C.,
a laser light input section that inputs a laser beam into the gas to be measured;
a laser light receiving section that receives the laser light that has passed through the gas to be measured;
a calculation unit that calculates the spatial distribution of the temperature and concentration of the gas to be measured based on the measured value of the laser light intensity in the laser light receiving unit;
A plurality of pairs of the laser light incident part and the laser light receiving part are provided,
The calculation unit is
A first step of discretely estimating the temperature and concentration of the gas to be measured within the internal space of the measurement chamber;
a second step of spatially interpolating the estimated values discretely estimated in the first step using a polynomial interpolation formula of order three or less;
Repeatedly correcting the estimated value so as to minimize the error between the laser light intensity calculated from the estimated value estimated in the first step and the measured value of the laser light intensity at the laser receiver. A third step of performing optimization calculations,
A fourth step of calculating the spatial distribution of temperature and concentration of the measured gas by increasing stepwise the number of points in the space of the estimated value corrected in the third step. , gas analyzer. Eight or more pairs of the laser light incident part and the laser light receiving part are provided,
7. The gas analyzer according to claim 6, wherein the laser light path between the laser light incident part and the laser light receiving part is configured to form a two-dimensional mesh within the gas to be measured. The gas analysis apparatus according to claim 6 or 7, wherein the calculation unit uses a bicubic convolutional interpolation method as the polynomial interpolation formula of order three or less in the second step. 9. The gas analysis apparatus according to claim 6, wherein the calculation unit uses a least squares method as the iterative optimization procedure in the third step. In the fourth step, the calculation unit sequentially divides the grid interval in the estimated value space into two as a step of increasing the number of points in the estimated value space in stages. The gas analyzer according to any one of claims 6 to 9, characterized by:

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