CN111487211A - Incoherent broadband cavity enhanced absorption spectrum fitting waveband selection method - Google Patents

Incoherent broadband cavity enhanced absorption spectrum fitting waveband selection method Download PDF

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CN111487211A
CN111487211A CN202010394233.XA CN202010394233A CN111487211A CN 111487211 A CN111487211 A CN 111487211A CN 202010394233 A CN202010394233 A CN 202010394233A CN 111487211 A CN111487211 A CN 111487211A
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凌六一
黄友锐
王成军
韦颖
韩涛
徐善永
唐超礼
周孟然
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Anhui University of Science and Technology
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Abstract

The invention discloses a fitting waveband selection method for an incoherent broadband cavity enhanced absorption spectrum, which is characterized by determining a nonlinear relation between two parameters, namely the width and the central wavelength of a fitting waveband, and a relative fitting uncertainty and a fitting residual standard deviation by using a BP neural network machine learning method, and then determining the fitting waveband according to the expected relative fitting uncertainty and the fitting residual standard deviation, and specifically comprises the following steps of: determining a broad spectral band; dividing the broad spectral band into a plurality of sub-bands having different widths and center wavelengths; fitting the sub-band absorption spectrum; normalizing the fitting result to form a data sample; establishing a BP neural network and performing network learning; and obtaining the width and the central wavelength of the wave band to be selected by utilizing the learned BP neural network, and finally obtaining the spectrum fitting wave band. Compared with the existing method, the method can obtain the optimal spectrum fitting wave band, and avoids the possibility of larger deviation of the fitting result of the existing method.

Description

Incoherent broadband cavity enhanced absorption spectrum fitting waveband selection method
Technical Field
The invention relates to a fitting waveband selection method of a broadband absorption spectrum, in particular to a fitting waveband selection method of an incoherent broadband cavity enhanced absorption spectrum.
Background
The incoherent wideband cavity reinforced absorption spectrum technology is one high sensitivity optical detection method, and has optical resonant cavity comprising high reflectivity lens to increase the absorption optical path and raise the detection sensitivity of the detected gas. The technology selects an absorption spectrum with a certain wave band, and uses a least square method to fit a gas absorption cross section to obtain a measured absorption coefficient so as to obtain the molecular number concentration of the measured gas. In selecting the spectrum fitting band, the band in which the reflectivity of the lens is located, the band in which the radiation spectrum of the light source is located, and the band in which the strong absorption of the gas exists are generally considered. If there are overlapping regions in these three bands, the overlapping regions are typically used as spectral fit bands. At present, the incoherent broadband cavity enhanced absorption spectrum technology mainly adopts a light emitting diode as a light source, generally, the full width at half maximum of the light emitting diode is only 20-30 nm, the reflectivity of a lens of an optical resonant cavity is a function of wavelength, a large difference between the peak wavelength of the radiation spectrum of the light emitting diode light source and the peak wavelength of the reflectivity of the lens often occurs, and the full width at half maximum of the light emitting diode is very narrow, so that the overlapping degree of the wave bands of the light emitting diode and the lens is not high. For this situation, the existing spectrum fitting band selection method is a trial-and-error method, i.e. empirically selecting several fitting bands considered to be better, performing fitting comparison, and then using the band with the smallest uncertainty or fitting residual amplitude of the fitting result as the final spectrum fitting band. Because the number of the tried wave bands is limited, when the spectrum fitting wave band selected by the existing method is used for fitting the absorption spectrum, the uncertainty of the obtained fitting result or the fitting residual amplitude value does not necessarily reach the expected value of the measurement system, and especially when the overlapping area of the wave bands where the reflectivity of the lens, the radiation spectrum of the light source and the strong absorption of the gas exist is small, the fitting result of the spectrum fitting wave band selected by the existing method for the concentration of the gas to be measured may generate large deviation.
Disclosure of Invention
The invention aims to solve the problem that the fitting result of the existing spectrum fitting waveband selection method for the incoherent broadband cavity enhanced absorption spectrum technology to the concentration of a gas to be measured may generate large deviation, and provides a spectrum fitting waveband selection method based on BP neural network machine learning.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention discloses a fitting waveband selection method of an incoherent broadband cavity enhanced absorption spectrum, which is characterized in that a BP neural network machine learning method is utilized to determine a nonlinear relation between two parameters of the width and the center wavelength of a fitting waveband and a relative fitting uncertainty and a fitting residual standard deviation, and then the fitting waveband is determined according to an expected relative fitting uncertainty and the fitting residual standard deviation, and specifically comprises the following steps:
the first step is as follows: determining a wide spectral band according to an incoherent broadband cavity enhanced absorption spectrum measurement system; assuming that the wave band is [ a, b ], wherein a is the minimum wavelength, b is the maximum wavelength, and the difference between b and a is not less than 30nm and is an even number;
the second step is that: in the wave bands [ a, b]Internally divided into a plurality of sub-bands
Figure BDA0002486799280000021
Wherein, BWjIs the width of the sub-band or sub-bands,
Figure BDA0002486799280000022
λijis the center wavelength of the sub-band,
Figure BDA0002486799280000023
Figure BDA0002486799280000024
the third step: selecting waveletsSegment of
Figure BDA0002486799280000025
As a spectrum fitting wave band, fitting the absorption cross section of the gas to be measured to the measured absorption coefficient by adopting a least square method to obtain a fitting concentration value N corresponding to all sub-wave bandsijUncertainty of fit EijAnd standard deviation of fit residual Dij(ii) a Calculating relative fit uncertainty REij，
Figure BDA0002486799280000026
The fourth step: sample data, i.e. sub-band width BW, by using maximum-minimum normalization methodjCentral wavelength of sub-band lambdaijRelative fit uncertainty REijAnd fitted residual standard deviation DijNormalization processing is carried out, and the normalized results are respectively
Figure BDA0002486799280000027
And
Figure BDA0002486799280000028
the fifth step: establishing BP neural network, the number of nodes of network input layer is 2, and the input quantity is respectively
Figure BDA0002486799280000029
And
Figure BDA00024867992800000210
the number of nodes of the network output layer is 2, and the output quantity is
Figure BDA00024867992800000211
The number of nodes of the network hidden layer can be adjusted according to the training result; dividing a data sample corresponding to input-output quantity into a learning set and a testing set, and learning and testing the BP neural network;
and a sixth step: uncertainty RE of expected relative fit using max-min normalizationEAnd standard deviation of fit residual DEGo on to returnIs subjected to a normalization treatment to obtain
Figure BDA00024867992800000212
And
Figure BDA00024867992800000213
obtaining the expected sub-band width with normalized output quantity of the network as the input quantity of the learned BP neural network
Figure BDA00024867992800000214
Sum sub-band center wavelength
Figure BDA00024867992800000215
The seventh step: for normalized expected sub-band width
Figure BDA00024867992800000216
Sum sub-band center wavelength
Figure BDA00024867992800000217
Performing inverse normalization to obtain the desired sub-band width BWESum sub-band center wavelength λE(ii) a The finally determined spectral fit band is
Figure BDA00024867992800000218
Figure BDA00024867992800000219
The invention has the advantages and beneficial effects that:
(1) according to the method, a plurality of sub-wave bands with different widths and central wavelengths are selected in a specific wave band to serve as the spectrum fitting wave band, so that a large number of data samples representing the relevance between the fitting wave band and the fitting result are obtained, the relation between the data samples is mined, and the relevance between the data samples is more scientific than that obtained by the conventional method through experience.
(2) According to the method, after the nonlinear relation between the fitting wave band and the fitting result is obtained through a machine learning method, the optimal spectrum fitting wave band can be obtained according to the uncertainty of the fitting result and the specific requirements of the fitting residual error, and the possibility that the fitting result of the existing method generates larger deviation is avoided.
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FIG. 1 is a flow chart of the operation of the present invention.
Detailed Description
The method determines the nonlinear relation between two parameters of the width and the center wavelength of the fitting wave band and the relative fitting uncertainty and the standard deviation of the fitting residual by using a BP neural network machine learning method, and then determines the fitting wave band according to the expected relative fitting uncertainty and the standard deviation of the fitting residual.
As shown in FIG. 1, the method for selecting the fitting band of the incoherent broadband cavity enhanced absorption spectrum of the present invention has seven steps, namely step 1 to step 7. In step 1, a wide spectrum wave band [ a, b ], [ a, b ] is determined according to a wave band where the reflectivity of a lens of the incoherent broadband cavity enhanced absorption spectrum measurement system is located, a wave band where a light source radiation spectrum is located and a wave band where strong absorption exists in gas, the three wave bands are covered as far as possible, and the difference value between b and a is not less than 30nm and is an even number.
In step 2, the spectral bands [ a, b ]]The method comprises the following steps of dividing the optical fiber into sub-bands with different widths and central wavelengths: the sub-band width is selected first, starting at 10nm and one step every 2nm until b-a. Thus, the width BW of a sub-bandjCan be expressed as:
Figure BDA0002486799280000031
then, in [ a, b ]]All possible center wavelengths are selected for each width sub-band in 1nm steps between. For example, if a is 430 and b is 460, the sub-band widths may range from 10,12,14, …, and 30 nm. For a sub-band of 10nm width, all possible center wavelengths are 435,436,437, …, 455nm, i.e. all sub-bands divided into 10nm width are: [430,440]，[431,441]，[432,442]，…，[450,460]And (5) nm. Sub-bands of other widths, and so on. Thus, the center wavelength λ of the sub-bandijCan be expressed as:
Figure BDA0002486799280000032
Figure BDA0002486799280000033
in step 3, the absorption cross section of the measured gas can be obtained by performing convolution operation on the instrument function of the spectrometer adopted by the incoherent broadband cavity enhanced absorption spectrum measurement system and the high-resolution absorption cross section of the measured gas given in the literature. The absorption coefficient is enhanced by the incoherent broadband cavity and the absorption spectrum measuring system according to the formula
Figure BDA0002486799280000034
(Note: α (. lamda.) is the absorption coefficient of the measured gas; I (. lamda.) and I0(λ) is the gas absorption spectrum and the reference spectrum, respectively; r (lambda) is the lens reflectivity; d is the length of the optical cavity). Taking all the sub-bands obtained by division in the step 2 as spectrum fitting bands, fitting the absorption cross section of the gas to be measured to the absorption coefficient by adopting a least square fitting method, and obtaining a fitting concentration value NijUncertainty of fit EijAnd standard deviation of fit residual Dij(ii) a According to the formula
Figure BDA0002486799280000035
Calculating to obtain relative fitting uncertainty REij。
In step 4, BW is normalized by max-min normalizationj、λij、REijAnd DijNormalization is carried out to obtain
Figure BDA0002486799280000036
Figure BDA0002486799280000037
And
Figure BDA0002486799280000038
the method specifically comprises the following steps:
Figure BDA0002486799280000039
Figure BDA00024867992800000310
wherein min represents the minimum value of the data set, and max represents the maximum value of the data set.
In step 5, a BP neural network containing an input layer, a hidden layer and an output layer is built by using MAT L AB, and the BP neural network obtained in step 4 is used
Figure BDA0002486799280000041
And
Figure BDA0002486799280000042
as an input to the network, a network interface is provided,
Figure BDA0002486799280000043
as a network output. And (4) dividing all data samples corresponding to the network input-output quantity obtained in the step (3) and the step (4) into a learning set and a testing set according to a certain proportion, and learning and testing the BP neural network.
In step 6, the expected relative fit uncertainty RE is normalized using a maximum-minimum methodEAnd standard deviation of fit residual DENormalization is carried out to obtain
Figure BDA0002486799280000044
And
Figure BDA0002486799280000045
the method specifically comprises the following steps:
Figure BDA0002486799280000046
will be provided with
Figure BDA0002486799280000047
And
Figure BDA0002486799280000048
inputting the data into the learned BP neural network obtained in the step 5, and outputting the data through the BP neural network to obtain
Figure BDA0002486799280000049
And
Figure BDA00024867992800000410
in step 7, the normalized expected sub-band width obtained in step 6 is used
Figure BDA00024867992800000411
Sum sub-band center wavelength
Figure BDA00024867992800000412
Performing inverse normalization to obtain the desired sub-band width BWESum sub-band center wavelength λEThe method specifically comprises the following steps:
Figure BDA00024867992800000413
Figure BDA00024867992800000414
thus, the final determined spectral fit band is
Figure BDA00024867992800000415
And ending the whole incoherent broadband cavity enhanced absorption spectrum fitting waveband selection process.

Claims (1)

1. The fitting wave band selection method of the incoherent broadband cavity enhanced absorption spectrum is characterized by comprising the following steps: determining a nonlinear relation between two parameters of the width and the center wavelength of a fitting waveband and a relative fitting uncertainty and a fitting residual standard deviation by using a BP neural network machine learning method, and then determining the fitting waveband according to the expected relative fitting uncertainty and the fitting residual standard deviation, wherein the method specifically comprises the following steps:
the first step is as follows: determining a wide spectral band according to an incoherent broadband cavity enhanced absorption spectrum measurement system; assuming that the wave band is [ a, b ], wherein a is the minimum wavelength, b is the maximum wavelength, and the difference between b and a is not less than 30nm and is an even number;
the second step is that: in the wave bands [ a, b]Internally divided into a plurality of sub-bands
Figure FDA0002486799270000011
Wherein, BWjIs the width, BW, of a sub-bandj＝10+2j，
Figure FDA0002486799270000012
λijIs the center wavelength of the sub-band,
Figure FDA0002486799270000013
i＝0，1，2，…，b-a-BWj；
the third step: selecting sub-bands
Figure FDA0002486799270000014
As a spectrum fitting wave band, fitting the absorption cross section of the gas to be measured to the measured absorption coefficient by adopting a least square method to obtain a fitting concentration value N corresponding to all sub-wave bandsijUncertainty of fit EijAnd standard deviation of fit residual Dij(ii) a Calculating relative fit uncertainty REij，
Figure FDA0002486799270000015
The fourth step: sample data, i.e. sub-band width BW, by using maximum-minimum normalization methodjCentral wavelength of sub-band lambdaijRelative fit uncertainty REijAnd fitted residual standard deviation DijNormalization processing is carried out, and the normalized results are respectively
Figure FDA0002486799270000016
And
Figure FDA0002486799270000017
the fifth step: establishing BP neural network, the number of nodes of network input layer is 2, and the input quantity is respectively
Figure FDA0002486799270000018
And
Figure FDA0002486799270000019
the number of nodes of the network output layer is 2, and the output quantity is
Figure FDA00024867992700000110
The number of nodes of the network hidden layer can be adjusted according to the training result; dividing a data sample corresponding to input-output quantity into a learning set and a testing set, and learning and testing the BP neural network;
and a sixth step: uncertainty RE of expected relative fit using max-min normalizationEAnd standard deviation of fit residual DECarrying out normalization treatment to obtain
Figure FDA00024867992700000111
And
Figure FDA00024867992700000112
obtaining the expected sub-band width with normalized output quantity of the network as the input quantity of the learned BP neural network
Figure FDA00024867992700000113
Sum sub-band center wavelength
Figure FDA00024867992700000114
The seventh step: for normalized expected sub-band width
Figure FDA00024867992700000115
Sum sub-band center wavelength
Figure FDA00024867992700000116
Performing inverse normalization to obtain the desired sub-band width BWESum sub-band center wavelength λE(ii) a The finally determined spectral fit band is
Figure FDA00024867992700000117
Figure FDA00024867992700000118
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CN103712939A (en) * 2013-12-30 2014-04-09 张显超 Pollutant concentration fitting method based on ultraviolet-visible spectrum
CN109001136A (en) * 2018-09-20 2018-12-14 杭州绿洁水务科技股份有限公司 A kind of COD on-line monitoring method based on ultraviolet visible light absorption spectrum
CN110414729A (en) * 2019-07-19 2019-11-05 西北农林科技大学 The potential maximum photosynthetic capacity prediction technique of plant based on characteristic wavelength
CN110991064A (en) * 2019-12-11 2020-04-10 广州城建职业学院 Soil heavy metal content inversion model generation method and system, storage medium and inversion method

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