JPS62157547A - Model mass analysis method by air dilution method of automobile emission - Google Patents

Abstract

PURPOSE:To achieve a higher measuring accuracy of component discharge at each running mode, by determining the flow rate of an emission gas by air dilution method to obtain the concentration of components to be inspected corresponding to the flow rate in the same phase by interpolation for correction. CONSTITUTION:The flow rate QE (t) of an emission gas is determined by subtracting the amount of diluted air QP (t) from the sum a fixed flow rate QA sucked to a gas analyzer and a fixed flow rate QM sucked with a sampler. The measurement of QP (t) is started immediately at a switch of a running mode (e.g.: idling IDL and acceleration ACC). On the other hand, the measurement of the concentration CE (t) of an object to be measured is started as delayed by a specified time (e.g.: tau1), based on a sampling data CES (t), a component concentration CEI (t) is determined corresponding in the same phase by interpolation. In addition, CE (t) is obtained by correction according to the formula I and by the formula II, the discharge M (t) of a object component is determined running mode wise. Wherein NC and NQ of the formula I represent sampling frequency of the concentration and flow rate in respective modes and rho of the formula II represents the density of the object component.

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial Application Field] The present invention is directed to the use of specific components in automobile exhaust gas; 2.
(N constant target components: co, cot, NOX, HC, etc.) driving mode (idling driving mode).

Regarding the modal mass analysis method using the air dilution amount method for measuring emissions in different modes (acceleration driving mode, constant speed driving mode, deceleration driving mode), please refer to the driving simulation test based on a predetermined driving mode switching sequence. Flow rate Qc(t) of exhaust gas discharged from a vehicle subjected to
, the amount of dilution air Qa (t) for the exhaust gas measured at a constant sampling time, and the constant flow rate Q^ drawn by a gas concentration analyzer for measuring the concentration of the component to be measured in the exhaust gas. and the constant flow IQII aspirated by the constant flow sampler, Qz (t)
−Qa +QN Qo (t)...■ In addition, the concentration CE(t) of the component to be measured in the exhaust gas is determined at the same constant sampling time as the flow rate QE(t) of the exhaust gas. M(t)−ρx C,, (t) X QE (t)
...(2) A vehicle based on the procedure of determining the emission amount M (t) of the component to be measured in the exhaust gas for each driving mode using the formula [where ρ is the density of the component to be measured] This paper relates to a modal mass analysis method using the air dilution amount method of exhaust gas.

[Conventional technology]

As a modal mass analysis method for automobile exhaust gas, in addition to the above-mentioned air dilution amount method, the exhaust gas flow rate QE (t) in the above equation 0 is used as the exhaust gas flow rate QE (t) after dilution and at a specific temperature Tt (
For example, using the flow rate of exhaust gas dehumidified at a temperature of 5°C (which is assumed to be constant by the system), and as the concentration CE(t) of the component to be measured in the above equation 0, after dilution and at a specific temperature T°C. The dilute stream method uses the measurement results of the concentration of the target component in the exhaust gas dehumidified at (for example, 5°C), and the exhaust gas flow rate QE (
t), the measurement result of C0z 4 degrees in exhaust gas dehumidified before dilution and at a specific temperature T ℃ (e.g. 5 ℃) and after dilution and dehumidified at a specific temperature T ℃ (e.g. 5 ℃) Co in the exhaust gas is determined by comparing the results of one measurement, and the concentration C of the component to be measured in the above formula 0 is calculated.
As E (t), the CO, trace method, etc., which uses the measurement result of the concentration of the component to be measured in the exhaust gas that has been dehumidified before dilution and at a specific temperature T°C (for example, 5°C), is well known. In either method, conventionally, the flow rate of the exhaust gas QD! The flow rate measurement to determine (t) is also
Concentration measurement for determining the concentration Cv (t) of the component to be measured was also performed with substantially no delay with respect to the switching time of each running mode, and at a common constant sampling time. In particular, in the modal mass analysis method using air dilution, which is the subject of the present invention, the measurement of the concentration CE(t) of each component to be measured is as follows:
As with other methods such as the Guilyutos Dream method and the Co, ) race method, the exhaust gas is dehumidified at a specific temperature T°C (for example, 5°C) by a dehumidifier installed before the gas concentration analyzer. However, the flow rate measurement for determining the exhaust gas flow IQE (t) is currently performed without any dehumidification.

[Problem that the invention seeks to solve]

However, the conventional method described above has the following serious drawbacks.

That is, FIG. 4 shows a driving mode (IDL near idling driving mode, A
CC: Accelerated operation mode, CRU: Constant speed operation mode, DE
C: Deceleration driving mode) and the flow NQ of exhaust gas from the vehicle measured in real time in response to switching changes.
This is a timing chart schematically showing the -a-like changes in E (t) and the concentration CE (t) of the component to be measured in the exhaust gas. As is clear from this figure, The flow fiat (t) changes with almost no lag / following the timing H,, Hx, H3,) (,) for each cut of the driving mode, but the concentration Cz (t) of the component to be measured changes. For example, due to response delays inherent in the piping system or gas concentration analyzer, adsorption/desorption phenomena of the component gas to be measured, etc., each switching timing H of the travel mode is
,,H,,H,, a certain amount of delay time τ1 from H4, respectively.
．． τ2. τ5. It can be seen that it changes with τ4.

Moreover, each of the weekly hours rl+τcustomer, τ1. Since τ4 is different for each driving mode and for each component to be measured, the data of the concentration CC(t) of the component to be measured output from the gas concentration analyzer in real time is It has a relatively expanded or compressed form.

However, even though such changes in data are real, conventionally they have been completely ignored and, for example, the fifth
As shown by the circle in the figure (which shows the case of acceleration operation mode ACC), in other words, as mentioned above, the measurement of the exhaust gas flow rate QE (t) also involves the concentration C of the component to be measured.
1(t) was also carried out synchronously with a common fixed sampling time, with virtually no delay in relation to the switching point of each driving mode, so there was no unnecessary measurement in each driving mode. or incorrect sampling data of the concentration CC(t) of the component to be measured is mixed,
The sampling data of the exhaust gas flow rate QE (t) and the sampling data of the concentration CE (t) of the component to be measured do not correspond 1:1 in terms of phase and number. Therefore, the average Even when using the averaging method to find the emission amount M of the component to be measured, the
An error of ~30% occurs, and if the instantaneous calculation method is used to sequentially calculate the emission amount M(t) of the component to be measured at each time, the error will be too large, and the resulting data will be almost impossible. The drawback was that they could not be hired.

In addition, in the modal mass analysis method using air dilution, which is the subject of the present invention, as described above, the concentration Cc(t) of each component to be measured is measured at a specific temperature T°C (for example, 5°C). Even though this is done on exhaust gas that has been dehumidified in Not only did this method further deteriorate the accuracy of the emissions of the components to be measured, but it also had the major drawback of not being able to compare the results with those obtained by other methods such as the Guilyutos Dream method, CO, and trace methods. .

However, in recent years, demands for improving the performance of automobiles have become increasingly strict due to exhaust gas control laws, energy conservation, etc., and in this sense, the instantaneous calculation method described above, which allows for more detailed studies, has been put into practical use. At present, research is eagerly awaited to improve t# (improve t# and simplify calculations) and to compare and examine the results with data from various methods that have been accumulated in the past.

The present invention has been made in view of the above-mentioned circumstances, and its purpose is to use an averaging method to obtain the average emission amount M of the component to be measured for each driving mode using a relatively simple calculation method. Of course, even when using the instantaneous calculation method that sequentially calculates the emission amount M(t) of the measurement target component at each time, the emission amount of the measurement target component in the exhaust gas can be measured with high accuracy. To provide a new modal mass analysis method using the air dilution amount method for automobile exhaust gas, which allows easy and reliable comparison of the results with those obtained by other methods such as the Guilyutos Dream method and the CO at trace method. It is in.

[Means for solving problems]

In order to achieve the above object, the present invention provides a modal mass analysis method using the air dilution amount method of automobile exhaust gas according to the basic procedure described at the beginning. QE (t)
In order to make the temperature C,(t) of the component to be measured correspond to 1:1, the dilution air amount QDl in the above equation (1) is
(t), the sampling data obtained by starting the measurement with virtually no delay at the time of switching each driving mode is used as is, while as the concentration ct (t) of the component to be measured, the The measurement start timing for each running mode of sampling is delayed by a predetermined set time according to the component to be measured and the running mode from the time of switching each running mode, and the sampling data C! of the concentration of the component to be measured is delayed. After finding the concentration Ci+(t) of the component to be measured that corresponds to the sampling data of the exhaust gas flow rate QE(t) from $(t) by interpolation, CE(t) = Cz+(t ) XNc
/Na -...(3) [Here, NC and NQ are the number of samplings of Cz (t) and QE (t) in each mode, respectively, and are determined in advance.] Based on the calculation formula The concentration is corrected by the data compression method or the data expansion method, and the exhaust gas flow rate QE(t) used in the above equation (2) is the flow rate QE(t) calculated from the above equation (1). ) in a dehumidified state at a specific temperature T° C., using a humidity-corrected value for the flow rate QET(1).

[Effect]

That is, in the modal mass analysis method using the air dilution amount method of automobile exhaust gas according to the present invention, as will be more clearly understood from the explanation of the embodiments described below, the actual measurement is performed at a predetermined constant sampling time. Set the sampling start delay time for the concentration of the component to be measured, and collect the sampling data C1 measured accordingly.
By applying a relatively simple calculation correction to (1) by applying interpolation and data compression or data expansion methods, the moment-by-moment emission amount of the component to be measured can be determined. The flow rate QE of the exhaust gas (
t) and the concentration C1(t) of the component to be measured are made to correspond to l:1 in terms of their phase relationship and number, and in addition, the exhaust gas flow rate QE (t) used in the above calculation formula ), the flow IQE (t) obtained from the above equation (1) is the flow 11Q! in a dehumidified state at a specific temperature T°C! Since the temperature-corrected value is used for t(t), the emission amount M(t) of the component to be measured can be obtained from time to time with very high precision using the above calculation formula, and therefore, based on the calculation result, The average emission amount M of the component to be measured for each driving mode can also be determined with extremely high accuracy. According to research results to date, it has been found that the measurement error can be improved from the conventional 20 to 30% to about 5%.

In this way, it has become possible to accurately measure not only the average value for each driving mode, but also moment-to-moment changes in the emissions of the target components in automobile exhaust gas.
It has become possible to examine in detail various performances of automobiles during transient operation.

Furthermore, as mentioned above, the flow rate QE(t) of exhaust gas used in the above calculation formula (2) is calculated by converting the flow rate QE (t) obtained from the above calculation formula (1) in a dehumidified state at a specific temperature T°C. Since a humidity-corrected value is used for the flow rate QEt(t)5, that specific temperature T°C is set as the dehumidification temperature (for example, 5°C) in other methods such as the Guilyutos Dream method or the CO2 tracing method. By doing so, it has become possible to easily conduct research by comparing the results obtained by this method with the data obtained from the various methods that have been accumulated in the past.

Furthermore, as described above, in the method of the present invention, the concentration CE (t) of the component to be measured and the flow rate QE (t
) is based on a relatively simple method, so a computer with a relatively small capacity is sufficient to implement it, and it is also cost effective when constructing a modal mass analysis system for automobile exhaust gas. Very advantageous.

〔Example〕

Specific embodiments of the present invention are shown below in the drawings (Figures 1 to 3).
This will be explained with reference to Figure).

FIG. 1 shows a schematic configuration of a modal mass analysis system using air dilution of automobile exhaust gas to which the method of the present invention is applied.

Reference numeral 1 denotes a chassis dynamometer as a vehicle driving simulator, which absorbs the force generated by the test vehicle 2 while keeping the vehicle body stationary.
It is configured to be able to simulate the state in which a vehicle is traveling on an actual road. Regarding this chassis dynamometer 1, for example, Japanese Patent Application No. 118681/1981 and Japanese Patent Application No. 142/1983 filed by the applicant of the present application
224, Japanese Patent Application No. 59-52657, etc., and is well known, so a detailed explanation of its configuration will be omitted here.

The test vehicle 2 is operated in various driving modes (I) based on a predetermined sequence by the chassis dynamometer 1.
DL near idling driving mode.

ACCF acceleration operation mode, CRU: constant speed operation mode, D
EC: deceleration operation mode).

3 is an inflow path for exhaust gas discharged from the test vehicle 2, and this exhaust gas inflow path 3 includes a heat exchanger 4. Constant flow venturi part 5. A constant flow sampler CvS consisting of a constant flow suction blower 6 and the like is connected, and the connection between the exhaust gas inflow path 3 and the constant flow sampler CvS includes:
A dilution air inflow path 9 in which a filter 7 and an ultrasonic flowmeter 8 are interposed are connected together.

From the exhaust gas inflow path 3, various specific component gases (such as Co and Co as components to be measured) in the exhaust gas are supplied.
A sampling channel 10 is provided for measuring the concentrations of t, NOK, HC, etc.), and the sampling channel 10 is filled with exhaust gas at a specific temperature (for example, 5° C.) in order from the upstream side. Dehumidifier 1 that removes moisture inside
1. Concentration analyzer 13 for the various specific component gases (components to be measured). A constant flow suction blower 14 is interposed.

For example, a minicomputer with relatively small capacity.
A system controller that performs calculations and controls for the chassis dynamometer 1, and also monitors the flow rate measurement results by the ultrasonic flowmeter 8 in the dilution air inflow path 9 and the concentration by the gas concentration analyzer 13. Based on the measurement results, one of the components to be measured in the exhaust gas is discharged! ! It is configured to perform arithmetic processing to obtain k (mass) for each driving mode (details thereof will be described later). Further, 15 is an input/output (Ilo) interface interposed between the system controller 14 and the chassis dynamometer 1, the ultrasonic flowmeter 8, and the gas concentration analyzer 13. Although not shown, the system controller 1
4 includes an operation panel, display device, recorder,
Needless to say, various related devices such as memory devices are connected.

Next, the arithmetic processing for calculating the emission amount (mass) of the component to be measured in the exhaust gas is executed by the system controller 14, that is, the principle of the modal mass analysis method using air dilution of automobile exhaust gas according to the present invention. I will explain about it.

That is, as shown in FIG. 1, the flow rate of the exhaust gas sucked into the concentration measurement sampling channel 10 is expressed as QA (
(constant), the amount of dilution air measured by the ultrasonic flow meter 8 in the dilution air inlet path 9 is Qo (t), and the total suction flow rate by the constant flow sampler CVS is QM (constant), then the amount of air discharged from the test vehicle 2 is QE is the flow rate of exhaust gas
(t) is QE (t) = QA + QH - Qo (
t)...It is obtained from the arithmetic expression ■.

On the other hand, if the concentration of the component to be measured in the exhaust gas measured by the gas concentration analyzer 13 is ci(t), then the emission amount (mass) of the component to be measured in the exhaust gas M (t) is M (t) =ρX CE (t) X QE (t)
...(2) [Here, ρ is the density of the component to be measured].

However, as explained using FIGS. 4 and 5 in the [Conventions] section, the exhaust gas flow rate QE
(t) is each switching timing of the driving mode H+, H
It changes following z, H3, and Ha almost without delay, but
The concentration C, (t) of the component to be measured changes with a certain amount of delay time τ1, τ, and τ1, τ4, respectively, than the driving mode switching timings H1 Hz, H2, and T(4). Each week's time τ9.τ years, τ3
．． Since τ4 is different for each driving mode and for each component to be measured, the data of the concentration C(1) of the component to be measured output in real time from the gas concentration analyzer 12 is different from the time axis in each driving mode. Since there is a general tendency for the exhaust gas to have a relatively expanded or compressed shape, in each driving mode, the exhaust gas QM 'l Q E
(t) and the measurement target component V; degree Cc(t) correspond to 1=1, the dilution air @ Q o (L) measured by the ultrasonic flowmeter 8 and the gas concentration analysis. The concentration ct (
The sampling of D and the processing of the sampling data are performed as follows.

That is, as shown in FIG. 2 (illustrating the case of acceleration driving mode ACC), the dilution air amount QD (t) in the above calculation formula (1) is set to The sampling data obtained by starting the measurement without delay is used as is [However, in the chart in Figure 2, this is expressed as the sampling result (indicated by ○) for the exhaust gas flow rate QE (t). ], On the other hand, the concentration C of the component to be measured in the above equation (2)
As E (t), the measurement start timing for each driving mode of the sampling is determined by a predetermined set time according to the component to be measured and the driving mode (in this example, τ1: this is determined experimentally in advance. ) from the point of failure in each driving mode, and based on the sampling data CEs (D (indicated by O) of the concentration of the component to be measured, the phase is the same as the sampling data of the exhaust gas flow WkQE (t). After finding the concentration CEI (t) (indicated by ・) of the corresponding component to be measured using the interpolation method, CE (t) = Cwt (t) X Nc
/NO...■ [Here, Nc and No are the sampling times of CE (t) and Qe (t) in each mode, respectively, which have also been determined experimentally in advance.] The density is corrected using the data compression method or data expansion method based on the formula.

By the way, as mentioned above, the concentration CE(
Although the measurement of t) was performed on exhaust gas dehumidified at a specific temperature T°C (for example, 5°C), the amount of dilution air QnC used to determine the flow rate QE(t) of exhaust gas is
Since the measurement of L) is performed without any dehumidification, in the method of the present invention, the exhaust gas flow rate QE(L) used in the above calculation formula (2) is determined by the calculation formula (1). ) at a specific temperature T
A humidity-corrected value is used for the flow IGet(t) in a dehumidified state at °C.

That is, the flow rate Q in the dehumidified state at that specific temperature T°C
Ey(t) is the flow ff obtained from the above equation (1)
1 qt (t), cotm degree a<t>, co□ concentration b(t) measured moment by moment by various gas concentration analyzers.
.

HC concentration C(t) and H* at the specific temperature T°C
It is obtained from the following calculation formula using the O concentration concentration color 7 and the CH ratio y of the fuel used.

In other words, to summarize the above, the modal mass analysis method using the air dilution amount method for automobile exhaust gas according to the present invention is as follows: M(t) = ρX CE (t) X CLtt(t)
...■ is the basic calculation formula, CE (t) = ct + (t) xNc /No -
・・■ and QE (t) =Qa +0M QD (t)
... ■ and etc. are used as auxiliary calculation expressions.

Next, with reference to FIG.
The measurement principle of (t) will be explained below.

That is, this ultrasonic flow meter 8 is basically for measuring flow velocity, and includes two sets of ultrasonic transceivers 8A and 8B that are arranged opposite to each other at an angle θ with respect to the dilution air inflow path 9.
It has the characteristic that it is not easily affected by pressure loss.

As shown in the figure, the distance between the ultrasonic transceivers 8A and 8B is calculated, and the ultrasonic transceiver 8A is connected to the ultrasonic transceiver 8.
The ultrasonic propagation velocity to B is tI, and the ultrasonic propagation velocity from the ultrasonic transceiver 8B to the ultrasonic transceiver 8A is 1. The angle between the central axis of the dilution air inflow path 9 and the ultrasonic propagation axes of the image sound wave transmitters/receivers 8A and 8B is θ, and the linear average flow velocity in the dilution air inflow path 9 is .

If the ultrasonic propagation speed in stationary gas is to, then L, = L
/ (t, +Vcos θ) tz −L/ (to −Vcos θ), so 2 cos e tI tz holds true.

Therefore, the cross-sectional average flow velocity in the dilution air inflow path 9 is (■). Therefore, the cross-sectional area of the dilution air inflow path 9 is S, the fluid temperature in the standard state is To, and the fluid pressure in the standard state is PO+. When the fluid temperature is T and the fluid pressure in the operating state is P, the dilution air amount QD (t
) is TxP.

It can be obtained from the following calculation formula.

〔Effect of the invention〕

As is clear from the detailed description above, according to the modal mass analysis method using the air dilution amount method of automobile exhaust gas according to the present invention, the sampling start delay time of the measurement target component concentration data is set, and the measurement Calculation is performed to obtain the momentary emission amount of the component to be measured by performing relatively simple calculation correction by applying interpolation and data compression or data expansion methods to the sampled data CEs(t). Flow rate QE (t) of the exhaust gas used in formula 〇 and concentration c of the component to be measured
i(t) in terms of their phase relationship and number of objects:
In addition, as the exhaust gas flow NQE (t) used in the arithmetic expression (2), the flow i1QA (1) obtained from the arithmetic expression (1) is set to a specific temperature T°C. Since the humidity-corrected value is used for the flow rate QEt(t) in the dehumidified state at Based on the calculation results, the average emission amount M of the component to be measured for each driving mode can also be determined with extremely high accuracy, making it possible to examine in detail various performances of the vehicle during transient operation. , as described above, the exhaust gas flow rate QE(t) used in the above calculation formula (2) is set to a specific temperature T°C.
Since we used a humidity-corrected value for the flow IQEy(t) in the dehumidified state at ℃), it is possible to easily conduct research by comparing the results of this method with the data of the various methods previously accumulated. Since the calculation correction regarding the concentration CE (t) of the component to be measured and the flow IQE (t) of the exhaust gas in is based on a relatively simple method, the computer used to implement it is relatively small in capacity. is enough,
Various excellent effects have been demonstrated, such as being very advantageous in terms of cost when constructing a modal mass analysis system for automobile exhaust gas.

[Brief explanation of drawings]

1 to 3 show a specific example of a modal mass analysis method using the air dilution amount method for automobile exhaust gas according to the method of the present invention, and FIG. 1 shows a modal mass analysis method using the air dilution amount method to which the method of the present invention is applied. Overall schematic configuration diagram of the mass analysis system,
FIG. 2 is a schematic timing chart for explaining the basic principle of the method of the present invention, and FIG. 3 is an explanatory diagram of the principle of an ultrasonic flowmeter. Further, FIGS. 1 and 5 are for explaining the technical background of the present invention and problems of the prior art,
FIG. 4 shows a general schematic timing chart of various data used for modal mass analysis, and FIG. 5 shows a schematic timing chart for explaining the conventional method. 2...Test vehicle, 8... Group current meter, 12...
...Gas concentration analyzer, CVS...Constant flow sampler.

Claims (1)

[Scope of Claims] [1] The flow rate Q_E(t) of exhaust gas discharged from a vehicle subjected to a driving simulation test based on a predetermined driving mode switching sequence is measured at a certain sampling time. Dilution air amount Q_D for
(t), and a constant flow rate Q sucked by the gas concentration analyzer for measuring the concentration of the component to be measured in the exhaust gas.
_A and the constant flow rate Q aspirated by the constant flow sampler
From _M, Q_E(t)=Q_A+Q_M−Q_D(
t)...(1), and the concentration C_E(t) of the component to be measured in the exhaust gas is measured at the same constant sampling time as the flow rate Q_E(t) of the exhaust gas. , M(t)=ρ×C_E(t)×Q_E(t)...(2
) [where ρ is the density of the component to be measured] Air dilution of automobile exhaust gas is based on the procedure of determining the emission amount M(t) of the component to be measured in the exhaust gas for each driving mode using the following calculation formula. In the modal mass analysis method using the quantitative method, the exhaust gas flow rate Q_E(t) used in the above calculation formula (2) in each driving mode and the concentration C_E of the component to be measured are
(t) in a 1:1 correspondence, the above calculation formula (1
) as the dilution air amount Q_D(t), the sampling data obtained by starting measurement with virtually no delay at the time of switching each driving mode is used as is, while the concentration C_E(t) of the component to be measured is t), the measurement start timing for each driving mode of the sampling is delayed by a predetermined set time according to the component to be measured and the driving mode from the time of switching each driving mode, and the sampling data C_E of the concentration of the component to be measured is
After finding the concentration C_E_I(t) of the component to be measured which corresponds to the sampling data of the exhaust gas flow rate Q_E(t) from _S(t) by interpolation,
E(t)=C_E_I(t)×N_C/N_Q...(
3) [Here, N_C and N_Q are the number of samplings of C_E(t) and Q_E(t) in each mode, respectively, and are determined in advance.] Data compression method or data expansion based on the calculation formula Furthermore, as the exhaust gas flow rate Q_E(t) used in the above calculation formula (2), the flow rate Q_E(t) obtained from the above calculation formula (1) is adjusted to a specific temperature T. A modal mass analysis method using an air dilution amount method for automobile exhaust gas, characterized in that a humidity-corrected value is used for the flow rate Q_E_T(t) in a dehumidified state at °C. [2] Flow rate Q in the dehumidified state at the specific temperature T°C
_E_T(t) is the flow rate Q_E(t) obtained from the above calculation formula (1), CO concentration a(t), CO_2 concentration b(t), which is measured from time to time by various gas concentration analyzers,
HC concentration c(t) and H_ at the specific temperature T°C
Using the 2O concentration d_T and the CH ratio y of the fuel used, Q_E_T=Q_E(t) [1+D_T-X(t)]X
(t)=(y/2 [a(t)+b(t)+3c(t)]
−4c(t))/(a(t)/3.8b(t)+1)]
-Claim No. 1 determined from the arithmetic expression (4)
A modal mass analysis method using the air dilution amount method for automobile exhaust gas described in .