CN106290094A - The mie being applied to airborne dust particulate matter on-line monitoring scatters quick calculation method - Google Patents

Abstract

The invention discloses a kind of mie being applied to airborne dust particulate matter on-line monitoring and scatter quick calculation method, comprise the steps: to calculate the scattering coefficient of particle, form scattering coefficient form；Set up particle diameter distribution mathematical model, the reasonable initial value of model parameter in selected optimized algorithm；Inverting particle size is distributed, and calculates particle concentration.The present invention calculates the theoretical scattering coefficient of particle in advance, uses the method tabled look-up to calculate for model parameter optimization, it is to avoid repeatedly loop computation, very big Reduction Computation time；Algorithm utilizes gridding method seek to carry out the rational model parameter initial value of optimized algorithm for the first time, accurately obtain the global minimum of object function with this；The model parameter initial value that non-first time is measured is set as the model optimum parameter that the last time calculates, and reduces iterations, increases arithmetic speed；Can adapt to that airborne dust particle size scope is big, the quick characteristic of concentration change, accomplish the real-time measurement to airborne dust particle concentration for measuring system.

Description

The mie being applied to airborne dust particulate matter on-line monitoring scatters quick calculation method

Technical field

The present invention relates to airborne dust technical field of measurement of particulate matter concentration, be specifically related to one and be applied to airborne dust granule The mie of thing on-line monitoring scatters quick calculation method.

Background technology

Atmospheric Grains source complexity, result of study shows, airborne dust is the weight causing Atmospheric Particulate Matter Want factor.Airborne dust particle size range is big, concentration change is quick, therefore the change of monitoring airborne dust need applied widely, Measuring speed is fast, can the method for On-line sampling system.

Light scattering method is measured particle concentration and is had that measuring speed is fast, device is the most easy to use, can accomplish The advantages such as measurement in real time.When the principle of light scattering refers to the particulate matter that light is irradiated in medium, mutual with medium Effect can deviate the direction of propagation, and scattering causes the decay of light in all directions.Light scattering feelings in all directions Condition depends on the parameters such as the refractive index of the wavelength of light, the particle diameter of particulate matter and particulate matter.Mie scattering theory It it is appointing of being derived by of the Maxwell equation of Germany scientist Gustav Mie classical fluctuation optical theory The angular distribution strict mathematical solution of scattered light intensity of the meaning uniform spherical particle of composition.By 100 years of researches with Development, especially with the development of computer science, Mie scattering theory has tended to ripe and has been applied to raw Produce practice.

Current practice is mainly angular scattering method, diffraction in the light scattering method that atmosphere particle concentration is measured Scattering method and total scattering (also known as transmission beam method, light extinction method or nephelometry).Conventional data processing method is Function lambda limiting process and stand-alone mode solution.The present invention limits solution for function, i.e. assumes that the size of granule is divided Cloth meets certain functional relationship, by the distribution of sizes of optimized algorithm continuous inverting reduction granule, and then obtains Particle concentration information.But at present because initial value is chosen improper and repeatedly calls Mie in data handling procedure Scattering function causes speed to reduce, and general each data processing time reaches more than 90s, greatly have impact on The response speed of instrument, it is impossible to meet the tracking measurement demand of airborne dust particle concentration.

Summary of the invention

For solving the problems referred to above, the invention provides a kind of mie being applied to airborne dust particulate matter on-line monitoring Scattering quick calculation method.

For achieving the above object, the technical scheme that the present invention takes is:

The mie being applied to airborne dust particulate matter on-line monitoring scatters quick calculation method, comprises the steps:

S1, the scattering coefficient of calculating particle, formation scattering coefficient form:

Refractive index m according to airborne dust and lambda1-wavelength λ_i(1≤i≤N) calculates based on Mie scattering theory The various particle diameter D that airborne dust space exists_jThe theoretical scattering coefficient k of particle under (1≤j≤M)_ext, form N*M KPT Scatter coefficient form:

$k_{ext}=\frac{2}{{\mathrm{\α}}^2}\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}(2n+1)\mathrm{Re}(a_n+b_n)$

In formula, α=π D_j/λ_iFor dimensional parameters, a_n、b_nFor m, D_j、λ_iFunction, by Mie scattering reason Opinion obtains, and repeats no more here；

S2, setting up particle diameter distribution mathematical model, in selected optimized algorithm, model parameter is the most initial Value:

S21, draft multi-modal mathematical model according to airborne dust sample data or gross data f(a₁,a₂,...,a_N, x), wherein a₁,a₂,...,a_NFor the model parameter of mathematical model, the number of parameter and incident illumination Number of wavelengths is equal, can adjust the number of lambda1-wavelength according to model parameter number；X is particle diameter；

S22, determine whether to measure first, if it is, use in the range of airborne dust concentration is reasonably distributed Gridding method finds the suitable initial value of object function parameter；If this measurement is not to measure first, then by upper One secondary data processes the initial value of the model parameter that the optimal models parameter obtained processes as data next time,

I.e. ${(a_1,a_2,...,a_N)}_n^0={(a_1,a_2,...,a_N)}_{n-1}^{best};$

S3, inverting particle size are distributed, calculating particle concentration:

S31, based on function limit solution, utilize particle concentration distributed model to combine particle theory scattering coefficient Calculate one group of turbidity value under each wavelength, with actual measurement turbidity value comparing calculation residual sum of squares (RSS), pass through Iterating of L-M optimized algorithm, finds and is distributed immediate particle model optimum parameter with actual particle；

S32, optimum parameter is updated to particle concentration distributed model, obtains fixing particle size range by integration The concentration information of interior particle.

Preferably, only there is bigger change in surveyed airborne dust particulate matter refractive index in the form of described step S1 gained It is altered during the monochromatic wavelength change changed or use, the only numerical value in adopting form when data process.

Preferably, concretely comprising the following steps of described step S22: according to the zone of reasonableness of airborne dust distributed model parameter, Zone of reasonableness equalization at each parameter is taken out L numerical value and is formed N-dimensional grid, total L^NIndividual grid node； Respectively with the mathematical model parameter value at each node as initial value, calculate each light path turbidity value and actual value Least residual quadratic sum ε, takes the wherein minimum model parameter initial value corresponding to ε as this densitometer The initial value calculated.

Preferably, the concretely comprising the following steps of described step S32:

1) relation of particle diameter distributed model parameter Yu turbidity τ is set to function expression

τ_i=g (a₁,a₂,...,a_N,λ_i)；

In formula, τ_iFor the turbidity value calculated under i-th optical wavelength, a₁,a₂,...,a_NFor model parameter, λ_iWavelength for i-th light path；

Maximum times K and the iteration result that arrange the iterative computation of L-M algorithm allow residual sum of squares (RSS) maximum Value ε_max；

2) residual sum of squares (RSS) ε of each light path turbidity value based on model parameter value and actual value is calculated；

$\mathrm{\ϵ}=\underset{i=1}{\overset{N}{\Σ}}|{\mathrm{\τ}}_i-{\mathrm{A\τ}}_i{|}^2$

In formula, ε is residual sum of squares (RSS), τ_iFor calculating the turbidity value under i-th optical wavelength, A τ_iFor reality Survey the turbidity value under i-th optical wavelength；

3) judge that whether current residual sum of squares (RSS) ε is less than allowing residual sum of squares (RSS) maximum ε_max, if Then redirect execution step 4)；Otherwise judge now iterations whether less than maximum times N of iterative computation, If it is this calculates rational iteration step length with L-M algorithm, updates model parameter a₁,a₂,...,a_NPrediction Value, redirects execution step 2)；Otherwise redirect execution step 4)；L-M optimized algorithm implement process Do not repeat them here；

4) last group model parameter a after iterative computation being terminated₁,a₂,...,a_NAs optimal models parameter； Optimal models parameter is updated to particle concentration distributed model, obtains particle in the range of fixing particle diameter by integration Concentration information.

The method have the advantages that

The present invention calculates the theoretical scattering coefficient of particle in advance, uses the method tabled look-up for model parameter optimization Calculate, it is to avoid repeatedly loop computation, very big Reduction Computation time；Algorithm utilize gridding method seek to carry out The rational model parameter initial value of optimized algorithm, accurately obtains the global minimum of object function with this； The model parameter initial value that non-first time is measured is set as the model optimum parameter that the last time calculates, and reduces repeatedly Generation number, increases arithmetic speed；Present invention can apply to airborne dust measuring concentration of granules in certain, it is possible to adapt to airborne dust Particle size scope is big, the quick characteristic of concentration change, is used for system of measuring and accomplishes airborne dust particulate matter dense The real-time measurement of degree.

Accompanying drawing explanation

Fig. 1 is the mie scattering quick calculation method that the embodiment of the present invention is applied to airborne dust particulate matter on-line monitoring The flow chart of middle step S1；

Fig. 2 is the mie scattering quick calculation method that the embodiment of the present invention is applied to airborne dust particulate matter on-line monitoring The flow chart of middle step S2；

Fig. 3 is the mie scattering quick calculation method that the embodiment of the present invention is applied to airborne dust particulate matter on-line monitoring The flow chart of middle step S3.

Detailed description of the invention

In order to make objects and advantages of the present invention clearer, below in conjunction with embodiment, the present invention is carried out Further describe.Should be appreciated that specific embodiment described herein only in order to explain the present invention, It is not intended to limit the present invention.

As Figure 1-3, a kind of airborne dust particulate matter on-line monitoring of being applied to is embodiments provided Mie scatters quick calculation method, comprises the steps:

S1, the scattering coefficient of calculating particle, formation scattering coefficient form:

Refractive index m according to airborne dust and lambda1-wavelength λ_i(1≤i≤N) calculates based on Mie scattering theory Go out the various particle diameter D that airborne dust space exists_jThe theoretical scattering coefficient k of particle under (1≤j≤M)_ext, formed N*M KPT Scatter coefficient form:

$k_{ext}=\frac{2}{{\mathrm{\α}}^2}\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}(2n+1)\mathrm{Re}(a_n+b_n)---\left(1\right)$

In formula, α=π D_j/λ_iFor dimensional parameters, a_n、b_nIt is m, D_j、λ_iFunction, by Mie scattering reason Opinion obtains, and repeats no more here；This form only in surveyed airborne dust particulate matter refractive index generation large change or It is altered during the monochromatic wavelength change used, the only numerical value in adopting form when data process.

S2, setting up particle diameter distribution mathematical model, in selected optimized algorithm, model parameter is the most initial Value:

S21, draft multi-modal mathematical model according to airborne dust sample data or gross data f(a₁,a₂,...,a_N, x), wherein a₁,a₂,...,a_NFor the model parameter of mathematical model, the number of parameter and incident illumination Number of wavelengths is equal, can adjust the number of lambda1-wavelength according to model parameter number；X is particle diameter.

S22, determine whether to measure first, if it is, use in the range of airborne dust concentration is reasonably distributed Gridding method finds the suitable initial value of object function parameter.According to the zone of reasonableness of airborne dust distributed model parameter, Zone of reasonableness equalization at each parameter is taken out L numerical value and is formed N-dimensional grid, total L^NIndividual grid node. Respectively with the mathematical model parameter value at each node as initial value, calculate each light path turbidity value and actual value Least residual quadratic sum ε (circular is shown in Part III), takes the wherein minimum mould corresponding to ε The initial value that type parameter initial value calculates as this concentration.If this measurement is not to measure first, then will Last data process the initial of the model parameter that the optimal models parameter obtained processes as data next time Value.

I.e. ${(a_1,a_2,...,a_N)}_n^0={(a_1,a_2,...,a_N)}_{n-1}^{best}---\left(2\right)$

S3, inverting particle size are distributed, calculating particle concentration:

S31, based on function limit solution, utilize particle concentration distributed model to combine particle theory scattering coefficient Calculate one group of turbidity value under each wavelength, with actual measurement turbidity value comparing calculation residual sum of squares (RSS), pass through Iterating of L-M optimized algorithm, finds and is distributed immediate particle model optimum parameter with actual particle；

S32, optimum parameter is updated to particle concentration distributed model, obtains fixing particle size range by integration The concentration information of interior particle.Specific implementation is as follows:

1) relation of particle diameter distributed model parameter Yu turbidity τ is set to function expression (3), arranges Maximum times K of the iterative computation of L-M algorithm and iteration result allow residual sum of squares (RSS) maximum ε_max；

τ_i=g (a₁,a₂,...,a_N,λ_i) (3)

In formula, τ_iFor the turbidity value calculated under i-th optical wavelength, a₁,a₂,...,a_NFor model parameter, λ_iWavelength for i-th light path；

2) residual sum of squares (RSS) ε of each light path turbidity value based on model parameter value and actual value is calculated；

$\mathrm{\ϵ}=\underset{i=1}{\overset{N}{\Σ}}|{\mathrm{\τ}}_i-{\mathrm{A\τ}}_i{|}^2---\left(4\right)$

In formula, ε is residual sum of squares (RSS), τ_iFor calculating the turbidity value under i-th optical wavelength, A τ_iFor reality Survey the turbidity value under i-th optical wavelength；

3) judge that whether current residual sum of squares (RSS) ε is less than allowing residual sum of squares (RSS) maximum ε_max, if Then redirect execution step 4)；Otherwise judge now iterations whether less than maximum times N of iterative computation, If it is this calculates rational iteration step length with L-M algorithm, updates model parameter a₁,a₂,...,a_NPrediction Value, redirects execution step 2)；Otherwise redirect execution step 4).L-M optimized algorithm implement process Do not repeat them here；

4) last group model parameter a after iterative computation being terminated₁,a₂,...,a_NAs optimal models parameter； Optimal models parameter is updated to particle concentration distributed model, obtains particle in the range of fixing particle diameter by integration Concentration information.

The above is only the preferred embodiment of the present invention, it is noted that common for the art For technical staff, under the premise without departing from the principles of the invention, it is also possible to make some improvements and modifications, These improvements and modifications also should be regarded as protection scope of the present invention.

Claims (4)

1. the mie being applied to airborne dust particulate matter on-line monitoring scatters quick calculation method, it is characterised in that Comprise the steps:

S1, the scattering coefficient of calculating particle, formation scattering coefficient form:

Refractive index m according to airborne dust and lambda1-wavelength λ_i(1≤i≤N) calculates based on Mie scattering theory The various particle diameter D that airborne dust space exists_jThe theoretical scattering coefficient k of particle under (1≤j≤M)_ext, form N*M KPT Scatter coefficient form:

$k_{ext}=\frac{2}{{\mathrm{\α}}^2}\underset{n=1}{\overset{\mathrm{\∞}}{\Σ}}(2n+1)\mathrm{Re}(a_n+b_n)$

In formula, α=π D_j/λ_iFor dimensional parameters, a_n、b_nFor m, D_j、λ_iFunction；

S2, setting up particle diameter distribution mathematical model, in selected optimized algorithm, model parameter is the most initial Value:

S21, draft multi-modal mathematical model according to airborne dust sample data or gross data f(a₁,a₂,...,a_N, x), wherein a₁,a₂,...,a_NFor the model parameter of mathematical model, the number of parameter and incident illumination Number of wavelengths is equal, can adjust the number of lambda1-wavelength according to model parameter number；X is particle diameter；

S22, determine whether to measure first, if it is, use in the range of airborne dust concentration is reasonably distributed Gridding method finds the suitable initial value of object function parameter；If this measurement is not to measure first, then by upper One secondary data processes the initial value of the model parameter that the optimal models parameter obtained processes as data next time,

I.e. ${(a_1,a_2,\mathrm{...},a_N)}_n^0={(a_1,a_2,\mathrm{...},a_N)}_{n-1}^{best};$

S3, inverting particle size are distributed, calculating particle concentration:

S31, based on function limit solution, utilize particle concentration distributed model to combine particle theory scattering coefficient Calculate one group of turbidity value under each wavelength, with actual measurement turbidity value comparing calculation residual sum of squares (RSS), pass through Iterating of L-M optimized algorithm, finds and is distributed immediate particle model optimum parameter with actual particle；

S32, optimum parameter is updated to particle concentration distributed model, obtains fixing particle size range by integration The concentration information of interior particle.

The mie scattering quickly meter being applied to airborne dust particulate matter on-line monitoring the most according to claim 1 Calculation method, it is characterised in that the form of described step S1 gained is only sent out in surveyed airborne dust particulate matter refractive index It is altered during the monochromatic wavelength change of raw large change or use, when data process only in adopting form Numerical value.

The mie scattering quickly meter being applied to airborne dust particulate matter on-line monitoring the most according to claim 1 Calculation method, it is characterised in that concretely comprising the following steps of described step S22: according to airborne dust distributed model parameter Zone of reasonableness, the zone of reasonableness equalization at each parameter is taken out L numerical value and is formed N-dimensional grid, total L^N Individual grid node；Respectively with the mathematical model parameter value at each node as initial value, calculate each light path turbidity Value and least residual quadratic sum ε of actual value, take the wherein minimum model parameter initial value corresponding to ε and make The initial value calculated for this concentration.

The mie scattering quickly meter being applied to airborne dust particulate matter on-line monitoring the most according to claim 1 Calculation method, it is characterised in that concretely comprising the following steps of described step S32:

1) relation of particle diameter distributed model parameter Yu turbidity τ is set to function expression

τ_i=g (a₁,a₂,...,a_N,λ_i)；

In formula, τ_iFor the turbidity value calculated under i-th optical wavelength, a₁,a₂,...,a_NFor model parameter, λ_iWavelength for i-th light path；

Maximum times K and the iteration result that arrange the iterative computation of L-M algorithm allow residual sum of squares (RSS) maximum Value ε_max；

2) residual sum of squares (RSS) ε of each light path turbidity value based on model parameter value and actual value is calculated；

$\mathrm{\ϵ}=\underset{i=1}{\overset{N}{\Σ}}|{\mathrm{\τ}}_i-{\mathrm{A\τ}}_i{|}^2$

In formula, ε is residual sum of squares (RSS), τ_iFor calculating the turbidity value under i-th optical wavelength, A τ_iFor reality Survey the turbidity value under i-th optical wavelength；

3) judge that whether current residual sum of squares (RSS) ε is less than allowing residual sum of squares (RSS) maximum ε_max, if Then redirect execution step 4)；Otherwise judge now iterations whether less than maximum times N of iterative computation, If it is this calculates rational iteration step length with L-M algorithm, updates model parameter a₁,a₂,...,a_NPrediction Value, redirects execution step 2)；Otherwise redirect execution step 4)；

4) last group model parameter a after iterative computation being terminated₁,a₂,...,a_NAs optimal models parameter； Optimal models parameter is updated to particle concentration distributed model, obtains particle in the range of fixing particle diameter by integration Concentration information.