JPH0634637A - Formation of calibration curve in gas analyzer - Google Patents

Abstract

PURPOSE:To easily and exactly obtain a calibration curve and prove justifiability of the obtained calibration curve by approximating the calibration curve on the of an output value corresponding to gas concentration to a polynomial expression and finding an error of its primary differential. CONSTITUTION:Gas for calibration different in concentration is supplied to a gas analyzer 3 through a gas separator 2 and at the time 4 on move values of output corresponding to gas concentration are taken. A calibration curve is approximated to a fourth order or less polynomial expression f (x) (x indicates analyzer output for showing concentration) by means of the least square method based on the value of 4 or more. A primary differential f' (x) of an approximate expression f (x) is checked within 1.05 times as large as the concentration of zero to a full scale. And, when f' (x) >=0 is indicated, a full scale error and a leading point error are found and the approximate expression f (x) is accepted as a calibration curve if these is within a range of an allowable error determined in a specific standard. Beyond the allowable range these are returned to the start, the approximate expression is found in the next order (for instance, a tertiary expression is used when a first fourth- order expression is approximated).

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for creating a calibration curve in a gas analyzer (hereinafter simply referred to as a method for creating a calibration curve).

[0002]

2. Description of the Related Art For example, as shown in FIG. 1, the calibration curve is prepared by supplying a calibration gas G from a calibration gas cylinder 1 to a gas divider 2 and using a calibration gas DG adjusted to an appropriate concentration. It is supplied to the analyzer 3 and the output signal x of the gas analyzer 3 is obtained. Then, conventionally, four or more measurement values are obtained as measurement points, and based on these measurement values, f (x) = a ₁ x + a ₂ x ² + a ₃ x ³ + A ₄ x ⁴ (a _{1 to} a ₄ are coefficients, and x is an analyzer output representing concentration) is approximated by a quartic equation, which is used as a calibration curve.

[0003] Figure 4 is a graph showing the concentration, the on coordinates taking the output on the vertical axis 4 and the measurement point p ₁ ~p ₄ and the calibration curve f (x) at that time on the horizontal axis.

[0004]

However, determining the coefficients a _{1 to} a ₄ of the quartic equation by using the least squares method requires a considerably skilled artisan technique, and the obtained calibration is necessary. It lacked a procedure to justify the curve.

The present invention has been made in view of the above matters, and an object thereof is to provide a method for obtaining a calibration curve more efficiently and more accurately than the conventional method. .

[0006]

In order to achieve the above object, a method for creating a calibration curve according to the present invention is such that a calibration gas having different concentrations is supplied to a gas analyzer,
At least four outputs corresponding to the gas concentration at that time are sampled. The calibration curve is approximated by a polynomial equation f (x) of fourth order or less using the least squares method based on the measured values of four or more (where x is (Analyzer output representing concentration), checking the first-order derivative f ′ (x) of the approximate expression f (x) within a range of concentration zero to 1.05 times full scale, f ′ (x) ≧ 0 At this time, a full scale error and a leading point error are respectively obtained, and it is determined whether or not both are within an allowable range defined by a specific standard.

[0007]

According to the above-described method for creating a calibration curve, anyone can easily obtain the calibration curve and at the same time prove the correctness of the obtained calibration curve, and obtain the calibration curve accurately. it can.

[0008]

Embodiments of the present invention will be described below with reference to the drawings. The apparatus used in the method for creating the calibration curve according to the present invention is no different from the apparatus used in the conventional method, and for example, the apparatus having the configuration shown in FIG. 1 is used.

The calibration gas DG having different concentrations is supplied to the gas analyzer 3 shown in FIG. 1, and 4 or more outputs corresponding to the gas concentration at that time are sampled, and based on the measured values of 4 or more, the minimum is obtained. Using the square method, the following N-order formula (N is 4 or less)
Is approximated by.

[0010]

[Equation 1]

The approximate expression f obtained in the above step
The first derivative f ′ (x) of (x) is checked in the range of x = 0 to 1.05 times full scale, and it is checked whether f (x) is an increasing function. (A) When f ′ (x) <0, that is, f (x)
If, for example, as shown in FIG. 2 (A), there is a part that decreases, a return is made to the above step, and an approximate expression is calculated by the following order. For example, first f
When (x) is approximated by a quartic equation, a cubic equation is obtained. (B) When f ′ (x)> 0, that is, f (x)
As shown in (A) of the same figure, when there is no part that decreases, the process proceeds to the next step.

By the way, in Japan, regulations such as quality control of a gas analyzer for analyzing exhaust gas comply with the control items stipulated by CFR (Code of Federal Regulations) in the United States. In this CFR,
The error range of the gas analyzer is defined as "a full-scale error is 1% or a reading point error is 2%, whichever is smaller."

Here, the full-scale error and the reading point error are defined by the following equations, respectively. Full scale error (%) = [(calculated concentration-generated concentration) /
Full scale concentration] × 100 Reading point error (%) = [(calculated concentration−generated concentration) / generated concentration] × 100 The calculated concentration refers to the concentration on the obtained calibration curve, and the generated concentration is It is the concentration of the calibration gas DG generated in the gas divider 2 and supplied to the gas analyzer 3.

Then, in other words, the above rules are as follows. That is, if the full scale is less than 50%, the reading point error is within 2% and the full scale is 50%.
In the above, the full-scale error must be within 1%. FIG. 3 shows this, and the shaded area is the allowable error range.

When the full-scale error and the leading point error in the approximate expression f (x) are within the error allowable range shown in FIG. 3, the approximate expression f
(X) is adopted as the calibration curve. On the other hand, when the f (x) is out of the allowable error range, the process returns to the step and the approximation is performed with the next order.

If none of the approximation formulas of the first to fourth orders can pass the criterion of the step, the calibration gas DG having different concentrations is supplied again to the gas analyzer 3 at that time. That is, four or more outputs corresponding to the gas concentration of are collected, and the calibration is performed again.

The processes of the steps up to the above are shown in FIG.
It is performed based on a program in the CPU 4 shown in FIG.

In the above-described embodiment, in the step, the quartic equation is first created as an approximate expression, but instead of this, a first-order or quadratic approximate expression may be created first. Good.

[0019]

As described above, according to the present invention,
It has become possible to create a calibration curve within the accuracy required by a specific standard more accurately and efficiently than the conventional method.

[Brief description of drawings]

FIG. 1 is a diagram showing an example of an apparatus used to create a calibration curve.

2A and 2B are diagrams each showing an example of a calibration curve.

FIG. 3 is a diagram showing an example of an allowable error range.

FIG. 4 is a diagram for explaining a conventional method.

[Explanation of symbols]

 3 ... Gas analyzer, DG ... Calibration gas, x ... Output.

Claims (1)

[Claims] 1. A calibration gas having different concentrations is supplied to a gas analyzer, and four or more outputs corresponding to the gas concentrations at that time are sampled. The least squares method is used based on the four or more measured values. Then, the calibration curve is approximated by a polynomial f (x) of 4th order or less (x is an analyzer output representing concentration), and the first-order derivative f ′ (x) of the approximate expression f (x) is zero concentration to full scale. Check within the range of 1.05 times, when f '(x) ≥ 0, determine the full-scale error and the reading point error respectively, and determine whether they are both within the allowable range specified by a specific standard. A method of creating a calibration curve in a gas analyzer, characterized by comprising a procedure of determining whether or not.