CN106290094B - Mie applied to fugitive dust particulate matter on-line monitoring scatters quick calculation method - Google Patents
Mie applied to fugitive dust particulate matter on-line monitoring scatters quick calculation method Download PDFInfo
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Abstract
The invention discloses a kind of mie applied to fugitive dust particulate matter on-line monitoring to scatter quick calculation method, includes the following steps: the scattering coefficient for calculating particle, forms scattering coefficient table；Particle diameter distribution mathematical model is established, the reasonable initial value of model parameter in optimization algorithm is selected；The distribution of inverting particle diameter, calculates particle concentration.The present invention calculates the theoretical scattering coefficient of particle in advance, is calculated using the method tabled look-up for model parameter optimization, avoids multiple loop computation, very big Reduction Computation time；Seek the rational model parameter initial value of progress first time optimization algorithm in algorithm, using gridding method with this accurate global minimum for obtaining objective function；The model parameter initial value of non-first time measurement is set as the optimal models parameter of last calculating, reduces the number of iterations, increases arithmetic speed；It can adapt to that fugitive dust particle size range is big, concentration changes quick characteristic, accomplish the real-time measurement to fugitive dust particle concentration for measuring system.
Description
Technical field
The present invention relates to fugitive dust technical field of measurement of particulate matter concentration, and in particular to it is online that one kind is applied to fugitive dust particulate matter
The mie of monitoring scatters quick calculation method.
Background technique
Atmospheric Grains source is complicated, and result of study shows that fugitive dust is an important factor for causing Atmospheric Particulate Matter.
Fugitive dust particle size range is big, concentration variation quickly, therefore monitors fugitive dust variation and needs that applied widely, measuring speed is fast, can be online
The method of real-time measurement.
Fast, device is simply easy to use with measuring speed for light scattering method measurement particle concentration, can accomplish to survey in real time
The advantages that amount.When the principle of light scattering refers to that illumination is mapped to the particulate matter in medium, propagation side can be deviateed with medium interaction
To scattering leads to the decaying of light in all directions.The scattering situation of light in all directions depends on the partial size of the wavelength of light, particle
And the parameters such as refractive index of particle.Mie scattering theory is the classical fluctuation optical theory of Germany scientist Gustav Mie
The strict mathematical solution of the scattered light intensity angle distribution of the uniform spherical particle of any ingredient that Maxwell equation is derived by.Pass through
100 years of researches and development, especially with the development of computer science, Mie scattering theory has tended to be mature and has applied
In production practices.
Current practice is mainly angular scattering method, diffraction scattering method in the light scattering method that atmosphere particle concentration measures
With total scattering (also known as transmission beam method, light extinction method or nephelometry).Common data processing method is function lambda limiting process and independent mould
Formula solution.The present invention limits solution for function, i.e. the size distribution of postulated particle meets some functional relation, calculated by optimization
The size of the continuous inverting of method also primary particle is distributed, and then obtains particle concentration information.But because just in current data handling procedure
Value is chosen improper and calls Mie scattering function that speed is caused to reduce repeatedly, and general each data processing time reaches 90s or more,
It greatly affected the response speed of instrument, be not able to satisfy the tracking measurement demand of fugitive dust particle concentration.
Summary of the invention
To solve the above problems, the present invention provides a kind of mie scattering applied to fugitive dust particulate matter on-line monitoring is quick
Calculation method.
To achieve the above object, the technical scheme adopted by the invention is as follows:
Mie applied to fugitive dust particulate matter on-line monitoring scatters quick calculation method, includes the following steps:
S1, the scattering coefficient for calculating particle form scattering coefficient table:
According to the refractive index m of fugitive dust and lambda1-wavelength λi, wherein 1≤i≤N, calculates fugitive dust based on Mie scattering theory
Various partial size D existing for spacej, wherein 1≤j≤M, and calculate the theoretical scattering coefficient k of particle under the partial sizeext, form N*M
KPT Scatter coefficient table:
In formula, α=π Dj/λiFor dimensional parameters, an、bnFor m, Dj、λiFunction, obtained by Mie scattering theory, here not
It repeats again；
S2, particle diameter distribution mathematical model is established, selectes the reasonable initial value of model parameter in optimization algorithm:
S21, multi-modal mathematical model f (a is drafted according to fugitive dust sample data or gross data1,a2,...,aN, x),
Wherein a1,a2,...,aNNumber for the model parameter of mathematical model, parameter is equal with lambda1-wavelength quantity, is joined according to model
Measure the number of number adjustment lambda1-wavelength；X is particle diameter；
S22, judge whether it is and measure for the first time, if it is, being sought in fugitive dust concentration distribution zone of reasonableness using gridding method
Look for the suitable initial value of objective function parameter；If the secondary measurement is not to measure for the first time, last data processing is obtained
Initial value of the optimal models parameter as the model parameter of data processing next time,
I.e.
S3, the distribution of inverting particle diameter, calculate particle concentration:
S31, solution is limited based on function, is calculated respectively using particle concentration distributed model combination particle theory scattering coefficient
One group of turbidity value under a wavelength passes through changing repeatedly for L-M optimization algorithm with actual measurement turbidity value comparing calculation residual sum of squares (RSS)
In generation, is found and the optimal models parameter of the immediate particle model of practical particle distribution；
S32, optimal models parameter is updated to particle concentration distributed model, grain in fixed particle size range is obtained by integral
The concentration information of son.
Preferably, the resulting table of step S1 only occurs large change in surveyed fugitive dust particulate matter refractive index or makes
Monochromatic wavelength is altered when changing, the only numerical value in adopting form when data processing.
Preferably, the specific steps of the step S22 are as follows: according to the zone of reasonableness of fugitive dust distributed model parameter, each
The zone of reasonableness equalization of parameter takes out L numerical value and forms N-dimensional grid, shares LNA grid node；Respectively with each node at
Mathematical model parameter value is initial value, calculates the least residual quadratic sum ε of each optical path turbidity value and actual value, takes wherein the smallest
Initial value of the model parameter initial value as this concentration calculation corresponding to ε.
Preferably, the specific steps of the step S32 are as follows:
1) relationship of particle diameter distributed model parameter and turbidity τ are set as function expression
τi=g (a1,a2,...,aN,λi)；
In formula, τiFor the calculated turbidity value under i-th of optical wavelength, a1,a2,...,aNFor model parameter, λiIt is i-th
The wavelength of optical path；
The maximum times K and iteration result that the iterative calculation of L-M algorithm is arranged allow residual sum of squares (RSS) maximum value εmax；
2) the residual sum of squares (RSS) ε of each optical path turbidity value based on model parameter value and actual value is calculated；
In formula, ε is residual sum of squares (RSS), τiTo calculate the turbidity value under i-th of optical wavelength, A τiTo survey i-th of optical wavelength
Under turbidity value；
3) judging whether current residual sum of squares (RSS) ε is less than allows residual sum of squares (RSS) maximum value εmax, if it is jump and hold
Row step 4)；Otherwise judge whether the number of iterations at this time is less than the maximum times N of iterative calculation, if it is this uses L-M algorithm
Reasonable iteration step length is calculated, model parameter a is updated1,a2,...,aNPredicted value, jump execute step 2)；Otherwise it jumps and holds
Row step 4)；Details are not described herein for the specific implementation process of L-M optimization algorithm；
4) by last group model parameter a after iterative calculation1,a2,...,aNAs optimal models parameter；It will most
Excellent model parameter is updated to particle concentration distributed model, obtains the concentration information of particle in fixed particle size range by integrating.
The invention has the following advantages:
The present invention calculates the theoretical scattering coefficient of particle in advance, is calculated using the method tabled look-up for model parameter optimization,
Avoid multiple loop computation, very big Reduction Computation time；Seek the conjunction of progress first time optimization algorithm in algorithm using gridding method
Model parameter initial value is managed, with this accurate global minimum for obtaining objective function；The model parameter of non-first time measurement is initial
Value is set as last calculated optimal models parameter, reduces the number of iterations, increases arithmetic speed；Present invention can apply to raise
Dirt measuring concentration of granules in certain, can adapt to that fugitive dust particle size range is big, concentration changes quick characteristic, be used for measuring system
Accomplish the real-time measurement to fugitive dust particle concentration.
Detailed description of the invention
Fig. 1 is that the embodiment of the present invention is applied to step in the mie scattering quick calculation method of fugitive dust particulate matter on-line monitoring
The flow chart of S1；
Fig. 2 is that the embodiment of the present invention is applied to step in the mie scattering quick calculation method of fugitive dust particulate matter on-line monitoring
The flow chart of S2；
Fig. 3 is that the embodiment of the present invention is applied to step in the mie scattering quick calculation method of fugitive dust particulate matter on-line monitoring
The flow chart of S3.
Specific embodiment
In order to which objects and advantages of the present invention are more clearly understood, the present invention is carried out with reference to embodiments further
It is described in detail.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to limit this hair
It is bright.
As shown in Figure 1-3, the embodiment of the invention provides a kind of mie scattering applied to fugitive dust particulate matter on-line monitoring is fast
Fast calculation method, includes the following steps:
S1, the scattering coefficient for calculating particle form scattering coefficient table:
According to the refractive index m of fugitive dust and lambda1-wavelength λi, wherein 1≤i≤N, calculates fugitive dust based on Mie scattering theory
Various partial size D existing for spacej, wherein 1≤j≤M, and calculate the theoretical scattering coefficient k of particle under the partial sizeext, form N*M
KPT Scatter coefficient table:
In formula, α=π Dj/λiFor dimensional parameters, an、bnIt is m, Dj、λiFunction, obtained by Mie scattering theory, here not
It repeats again；The table is only done when large change or the monochromatic wavelength used variation occur for surveyed fugitive dust particulate matter refractive index
Change, the only numerical value in adopting form when data processing.
S2, particle diameter distribution mathematical model is established, selectes the reasonable initial value of model parameter in optimization algorithm:
S21, multi-modal mathematical model f (a is drafted according to fugitive dust sample data or gross data1,a2,...,aN, x),
Wherein a1,a2,...,aNNumber for the model parameter of mathematical model, parameter is equal with lambda1-wavelength quantity, is joined according to model
Measure the number of number adjustment lambda1-wavelength；X is particle diameter.
S22, judge whether it is and measure for the first time, if it is, being sought in fugitive dust concentration distribution zone of reasonableness using gridding method
Look for the suitable initial value of objective function parameter.According to the zone of reasonableness of fugitive dust distributed model parameter, in the reasonable model of each parameter
It encloses impartial L numerical value of taking-up and forms N-dimensional grid, share LNA grid node.Respectively with the mathematical model parameter at each node
Value is initial value, calculates the least residual quadratic sum ε (circular is shown in Part III) of each optical path turbidity value and actual value,
Take initial value of the model parameter initial value as this concentration calculation corresponding to wherein the smallest ε.If the secondary measurement is not
It measures for the first time, then the optimal models parameter obtained last data processing is as the first of the model parameter of data processing next time
Initial value.
I.e.
S3, the distribution of inverting particle diameter, calculate particle concentration:
S31, solution is limited based on function, is calculated respectively using particle concentration distributed model combination particle theory scattering coefficient
One group of turbidity value under a wavelength passes through changing repeatedly for L-M optimization algorithm with actual measurement turbidity value comparing calculation residual sum of squares (RSS)
In generation, is found and the optimal models parameter of the immediate particle model of practical particle distribution；
S32, optimal models parameter is updated to particle concentration distributed model, grain in fixed particle size range is obtained by integral
The concentration information of son.Specific implementation is as follows:
1) relationship of particle diameter distributed model parameter and turbidity τ are set as function expression (3), setting L-M algorithm
The maximum times K and iteration result of iterative calculation allow residual sum of squares (RSS) maximum value εmax；
τi=g (a1,a2,...,aN,λi) (3)
In formula, τiFor the calculated turbidity value under i-th of optical wavelength, a1,a2,...,aNFor model parameter, λiIt is i-th
The wavelength of optical path；
2) the residual sum of squares (RSS) ε of each optical path turbidity value based on model parameter value and actual value is calculated；
In formula, ε is residual sum of squares (RSS), τiTo calculate the turbidity value under i-th of optical wavelength, A τiTo survey i-th of optical wavelength
Under turbidity value；
3) judging whether current residual sum of squares (RSS) ε is less than allows residual sum of squares (RSS) maximum value εmax, if it is jump and hold
Row step 4)；Otherwise judge whether the number of iterations at this time is less than the maximum times N of iterative calculation, if it is use L-M algorithm meter
Reasonable iteration step length is calculated, model parameter a is updated1,a2,...,aNPredicted value, jump execute step 2)；Otherwise execution is jumped
Step 4).Details are not described herein for the specific implementation process of L-M optimization algorithm；
4) by last group model parameter a after iterative calculation1,a2,...,aNAs optimal models parameter；It will most
Excellent model parameter is updated to particle concentration distributed model, obtains the concentration information of particle in fixed particle size range by integrating.
The above is only a preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art
For member, without departing from the principle of the present invention, it can also make several improvements and retouch, these improvements and modifications are also answered
It is considered as protection scope of the present invention.
Claims (4)
1. the mie for being applied to fugitive dust particulate matter on-line monitoring scatters quick calculation method, which comprises the steps of:
S1, the scattering coefficient for calculating particle form scattering coefficient table:
According to the refractive index m of fugitive dust and lambda1-wavelength λi, wherein 1≤i≤N, calculates fugitive dust space based on Mie scattering theory
Existing various partial size Dj, wherein 1≤j≤M, and calculate the theoretical scattering coefficient k of particle under the partial sizeext, form N*M particle
Scattering coefficient table:
In formula, α=π Dj/λiFor dimensional parameters, an、bnFor m, Dj、λiFunction；
S2, particle diameter distribution mathematical model is established, selectes the reasonable initial value of model parameter in optimization algorithm:
S21, multi-modal mathematical model f (a is drafted according to fugitive dust sample data or gross data1,a2,...,aN, x), wherein
a1,a2,...,aNNumber for the model parameter of mathematical model, parameter is equal with lambda1-wavelength quantity, according to model parameter
The number of number adjustment lambda1-wavelength；X is particle diameter；
S22, judge whether it is and measure for the first time, if it is, finding mesh using gridding method in fugitive dust concentration distribution zone of reasonableness
The suitable initial value of scalar functions parameter；If the secondary measurement is not to measure for the first time, last data processing is obtained optimal
Initial value of the model parameter as the model parameter of data processing next time,
I.e.
S3, the distribution of inverting particle diameter, calculate particle concentration:
S31, solution is limited based on function, calculates each wave using particle concentration distributed model combination particle theory scattering coefficient
One group of turbidity value under long is looked for actual measurement turbidity value comparing calculation residual sum of squares (RSS) by iterating for L-M optimization algorithm
To the optimal models parameter with the immediate particle model of practical particle distribution；
S32, optimal models parameter is updated to particle concentration distributed model, obtains particle in fixed particle size range by integrating
Concentration information.
2. the mie according to claim 1 applied to fugitive dust particulate matter on-line monitoring scatters quick calculation method, feature
It is, the monochromatic light that the resulting table of step S1 only occurs large change or use in surveyed fugitive dust particulate matter refractive index
It is altered when wavelength change, the only numerical value in adopting form when data processing.
3. the mie according to claim 1 applied to fugitive dust particulate matter on-line monitoring scatters quick calculation method, feature
It is, the specific steps of the step S22 are as follows: according to the zone of reasonableness of fugitive dust distributed model parameter, in the reasonable of each parameter
Range equalization takes out L numerical value and forms N-dimensional grid, shares LNA grid node；Joined respectively with the mathematical model at each node
Magnitude is initial value, calculates the least residual quadratic sum ε of each optical path turbidity value and actual value, takes corresponding to wherein the smallest ε
Initial value of the model parameter initial value as this concentration calculation.
4. the mie according to claim 1 applied to fugitive dust particulate matter on-line monitoring scatters quick calculation method, feature
It is, the specific steps of the step S32 are as follows:
1) relationship of particle diameter distributed model parameter and turbidity τ are set as function expression τi=g (a1,a2,...,aN,λi)；
In formula, τiFor the calculated turbidity value under i-th of optical wavelength, a1,a2,...,aNFor model parameter, λiFor i-th of optical path
Wavelength；
The maximum times K and iteration result that the iterative calculation of L-M algorithm is arranged allow residual sum of squares (RSS) maximum value εmax；
2) the residual sum of squares (RSS) ε of each optical path turbidity value based on model parameter value and actual value is calculated；
In formula, ε is residual sum of squares (RSS), τiTo calculate the turbidity value under i-th of optical wavelength, A τiFor under i-th of optical wavelength of actual measurement
Turbidity value；
3) judging whether current residual sum of squares (RSS) ε is less than allows residual sum of squares (RSS) maximum value εmax, if it is jump and execute step
It is rapid 4)；Otherwise judge whether the number of iterations at this time is less than the maximum times N of iterative calculation, if it is calculated and closed with L-M algorithm
The iteration step length of reason updates model parameter a1,a2,...,aNPredicted value, jump execute step 2)；Otherwise execution step is jumped
4)；
4) by last group model parameter a after iterative calculation1,a2,...,aNAs optimal models parameter；By optimal mould
Type parameter is updated to particle concentration distributed model, obtains the concentration information of particle in fixed particle size range by integrating.
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| CN102353621A (en) * | 2011-06-28 | 2012-02-15 | 上海理工大学 | Measuring device and method of light scattering particles |
| CN103728229A (en) * | 2013-12-09 | 2014-04-16 | 太原科技大学 | Measuring device and method for measuring average particulate size and concentration of atmospheric particulates |
| CN104374677A (en) * | 2014-10-09 | 2015-02-25 | 南京市计量监督检测院 | Concentration measuring device and method for dust in large diameter range |
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| CN102353621A (en) * | 2011-06-28 | 2012-02-15 | 上海理工大学 | Measuring device and method of light scattering particles |
| CN103728229A (en) * | 2013-12-09 | 2014-04-16 | 太原科技大学 | Measuring device and method for measuring average particulate size and concentration of atmospheric particulates |
| CN104374677A (en) * | 2014-10-09 | 2015-02-25 | 南京市计量监督检测院 | Concentration measuring device and method for dust in large diameter range |
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