CN115659771B - Aerosol particle size inversion method based on laser radar - Google Patents
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Abstract
The invention discloses an aerosol particle size inversion method based on a laser radar, which belongs to the technical field of laser radar measurement and is used for inverting the aerosol particle size, and comprises the steps of establishing an objective function according to a mathematical model, optimizing a decision variable by utilizing the mathematical model through the objective function, searching an individual for enabling the objective function to reach an optimal solution by utilizing a genetic algorithm through judging a fitness function, and obtaining the probability of a corresponding particle size range so as to determine the particle size distribution of particles; carrying out population fitness evaluation calculation to ensure that the value of the fitness function is greater than or equal to zero and the minimum value of the objective function corresponds to the maximum value of the fitness function; designing a genetic operator and determining operation parameters of the genetic algorithm, and applying the genetic algorithm to the inversion problem of the particle size in particle size measurement. Compared with the prior art, the anti-noise performance of the particle size inversion result is improved. The influence of priori hypothesis information on the inversion result is reduced, and the calculation speed of the inversion process is improved.
Description
Technical Field
The invention discloses an aerosol particle size inversion method based on a laser radar, and belongs to the technical field of laser radar measurement.
Background
The atmospheric aerosol particle spectrum distribution refers to a distribution function of aerosol particle concentration or number along with the particle size, also called particle size distribution, and the theoretical basis of a particle size inverse algorithm applied by laser radar is generally a light scattering method. The light scattering method refers to a method of measuring particle diameters using interaction of light with particles, and is also classified into various types according to specific principles. If the diffraction phenomenon of light is utilized, the particle size can be inverted by measuring the forward diffraction light intensity distribution of the particles; the extinction coefficient of aerosol particles is measured by an extinction method, and the particle size is inverted by using the meter scattering principle. Because the extinction coefficient is just the measurement quantity of the laser radar, the extinction method can be applied to radar data, and the atmospheric aerosol particle size distribution of different areas can be obtained through inversion. There are also methods for inverting particle size by measuring the intensity of scattered light at different angles, which are commonly used with particle size spectrometers, if any, to invert particle radius using 90 degree scattered light intensity.
In the application of the laser radar field, the extinction method is a complex multi-solution problem, the known quantity is usually only the extinction coefficient and the backscattering coefficient of aerosol, but the refractive index, the concentration of particles, the component ratio and the like are unknown, so that a proper algorithm is required to be applied to obtain an inversion result with physical significance and smaller error. The corresponding inversion algorithms can be largely divided into two main categories, independent mode and dependent mode. The independent mode has the advantages that a particle distribution model is not needed to be assumed in advance, but the defects are obvious, the calculation speed is low, the noise is very sensitive, and the required input information amount is large; non-independent mode implementation requires that the particle size distribution of the particulate matter be assumed, that the computation be compact and that no solution without physical significance generally occur. However, if the actual gas particle distribution deviates greatly from the assumption, a large calculation error occurs, and the noise immunity is poor. Based on the non-independent mode, the improved genetic algorithm system can be used for obtaining an optimized parameter set required by inversion, so that the anti-noise performance of the inversion result is improved, and the influence of the hypothesis information on the inversion result is reduced.
Disclosure of Invention
The invention aims to provide an aerosol particle size inversion method based on a laser radar, which aims to solve the problems of large calculation error and weak noise resistance of the aerosol particle size inversion method in the prior art.
An aerosol particle size inversion method based on a laser radar comprises the following steps:
s1, solving a Fredholm first-class integral equation of particle size distribution, wherein the Fredholm first-class integral equation is as follows:
s2 for hypothesis
Performing genetic coding, randomly generating a group of initial strings, and determining the number of initial populationsMGenerating a random number for each cycle, and operating the initial string obtained in the previous time, and reserving the string meeting the requirements to be added into the initial population until the number of the initial population is reached; />
S3, establishing an objective function according to a mathematical model:
wherein n is a combination of the number of wavelengths of the multi-wavelength lidar system, < >>
Optimizing a mathematical model by using an objective function, wherein the optimized decision variable is +.>
And->
The constraint is thata<D<b，k>0；
S4, coding by using a floating point number method, and randomly generating a floating point number between 0 and 1 as a gene valued；
S5, determining an individual evaluation method, reversely coding and converting the chromosome strings into true values, mapping the true values to a variable value space, and then obtaining the gene valuesdThe corresponding independent variable real number isd*(b-a)-b；
S6, carrying out population fitness evaluation calculation to ensure that the value of a fitness function is greater than or equal to zero, the minimum value of an objective function corresponds to the maximum value of the fitness function, and taking the fitness function as Fit (f (x))=1/[ 1+c+f (x) ], wherein c=0 is a conservative estimated value of the minimum limit of the objective function, f (x) is an objective function value of a certain point in a solution space, the objective function established by corresponding to S3, and Fit (f (x)) is a fitness function value of a corresponding individual;
s7, designing a genetic operator and determining operation parameters of the genetic algorithm;
s8, completing a first generation operation flow of a genetic algorithm, evaluating the fitness of individuals of a new generation, leaving the father of the new generation and meeting the fitness requirement to enter the next generation, repeating the evolution process, searching the global optimal value of the particle size distribution function, further obtaining the probability of the corresponding particle size range, and determining the particle size distribution of aerosol particles.
S7 comprises the following steps:
s7.1, selecting operation uses a random competition selection operator, in random competition selection, selecting a pair of individuals according to a roulette selection mechanism each time, calculating the proportion of the fitness value of each individual to the fitness value of the individuals in the whole population, enabling the pair of individuals to compete, selecting the individuals with high fitness, and repeating the steps until the selection is full;
s7.2, performing cross operation by using a single-point cross operator, pairing individuals pairwise, randomly setting a cross point in an individual code string for each paired individual, and exchanging partial chromosomes of two paired individuals at the cross point according to the set cross probability so as to generate two new individuals;
s7.3, using a prime mutation operator, assigning each locus of an individual a mutation probability as a mutation point, and replacing each assigned mutation point with other allele values to generate a new generation of individuals.
Compared with the prior art, the invention has the following beneficial effects: the anti-noise performance of the particle size inversion result is improved. The influence of priori hypothesis information on the inversion result is reduced. The calculation speed of the inversion process is improved; the problem that the traditional genetic algorithm is easy to converge to a local optimal solution is avoided, and the global searching capability in the inversion process is improved.
Drawings
FIG. 1 is a technical flow chart of the present invention;
FIG. 2 is a genetic algorithm flow chart;
FIG. 3 is a normal distribution diagram of particle size distribution satisfaction of a subgroup of aerosol particles;
FIG. 4 is a particle size distribution obtained by a conventional method;
FIG. 5 is a graph showing the particle size distribution obtained by the method of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the technical solutions in the present invention will be clearly and completely described below, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
An aerosol particle size inversion method based on laser radar, as shown in fig. 1, comprises the following steps:
s1, solving a Fredholm first-class integral equation of particle size distribution, wherein the Fredholm first-class integral equation is as follows:
s2 for hypothesis
Performing genetic coding, randomly generating a group of initial strings, and determining the number of initial populationsMGenerating a random number for each cycle, and operating the initial string obtained in the previous time, and reserving the string meeting the requirements to be added into the initial population until the number of the initial population is reached;
s3, establishing an objective function according to a mathematical model:
wherein n is a combination of the number of wavelengths of the multi-wavelength lidar system, < >>
Optimizing a mathematical model by using an objective function, wherein the optimized decision variable is +.>
And->
The constraint is thata<D<b，k>0；
S4, coding by using a floating point number method, and randomly generating a floating point number between 0 and 1 as a gene valued；
S5, determining an individual evaluation method, reversely coding and converting the chromosome strings into true values, mapping the true values to a variable value space, and then obtaining the gene valuesdThe corresponding independent variable real number isd*(b-a)-b；
S6, carrying out population fitness evaluation calculation to ensure that the value of a fitness function is greater than or equal to zero, the minimum value of an objective function corresponds to the maximum value of the fitness function, and taking the fitness function as Fit (f (x))=1/[ 1+c+f (x) ], wherein c=0 is a conservative estimated value of the minimum limit of the objective function, f (x) is an objective function value of a certain point in a solution space, the objective function established by corresponding to S3, and Fit (f (x)) is a fitness function value of a corresponding individual;
s7, designing a genetic operator and determining operation parameters of the genetic algorithm;
s8, completing a first generation operation flow of a genetic algorithm, evaluating the fitness of individuals of a new generation, leaving the father of the new generation and meeting the fitness requirement to enter the next generation, repeating the evolution process, searching the global optimal value of the particle size distribution function, further obtaining the probability of the corresponding particle size range, and determining the particle size distribution of aerosol particles.
As in fig. 2, S7 includes:
s7.1, selecting operation uses a random competition selection operator, in random competition selection, selecting a pair of individuals according to a roulette selection mechanism each time, calculating the proportion of the fitness value of each individual to the fitness value of the individuals in the whole population, enabling the pair of individuals to compete, selecting the individuals with high fitness, and repeating the steps until the selection is full;
s7.2, performing cross operation by using a single-point cross operator, pairing individuals pairwise, randomly setting a cross point in an individual code string for each paired individual, and exchanging partial chromosomes of two paired individuals at the cross point according to the set cross probability so as to generate two new individuals;
s7.3, using a prime mutation operator, assigning each locus of an individual a mutation probability as a mutation point, and replacing each assigned mutation point with other allele values to generate a new generation of individuals.
To facilitate an understanding of the present invention, some related theories are presented below.
The theoretical basis of extinction is the principle of Mie scattering and the Labert-Beer law. As light propagates in the medium, the light intensity decays according to the following equation:
wherein->
Indicating the intensity of light->
Indicating turbidity, & lt + & gt>
Indicating the optical path length.
Assuming that the spatial distribution of the population of particles in the medium is disordered and uniform, i.e. turbidity
And optical path->
Irrespective, integration along the optical path, one can get +.>
The transmitted light intensity is +.>
If the particles to be measured are spherical particles and the light scattering of the individual particles satisfies uncorrelated single scattering, then N particles have a particle size D and a light-receiving area ofsIs composed of monodisperse particlesTurbidity caused by scattering and absorption of light is +.>
. In (1) the->
Is the extinction coefficient, is the wavelength of incident light +.>
Particle diameter to be measured->
Particle complex refractive index->
Can be calculated from the rice scattering theory. Substituting the obtained product into the above-mentioned formula to obtain the product,
；
ratio of
Referred to as extinction values. In practice, the particles to be measured are not monodisperse but rather polydisperse particles with a range of size distribution, in which case the turbidity of the medium is +.>
；
Then the solution is carried out, so that,
；
to obtain a particle size distribution function
The equation needs to be solved, and the equation is a first Fredholm equation which cannot be theoretically solved at present and can only be solved in a numerical mode。
Aiming at the defects that the inversion result in the non-independent mode is influenced by a presupposed distribution model and the noise immunity is poor, an improved genetic algorithm is introduced to improve the noise immunity of the inversion result and reduce the dependence of the inversion result on priori information.
Where the left side is the measured value and the right side is the theoretical calculated value. Because the measurement inevitably has errors and the distribution of the particle system does not completely accord with a certain distribution function, the two parameters of the particle size and the extinction coefficient cannot be completely equal, the problem is to be solved as to how to select the two parameters of the particle size and the extinction coefficient, the two parameters can be converted into a constrained optimization problem, namely, the value of the optimal characteristic particle size parameter can be found by optimizing search by a computer, and the objective function is the minimum. However, most of the commonly used optimization algorithms are local optimization algorithms, and the problem to be solved is a multi-value problem, so that a global minimum point is required. The global optimal solution is found through selection, crossover, inheritance and other genetic algorithms which reflect the reproduction characteristics in the biosphere.
Control parameter selection in genetic algorithm: setting the initial population scale as 100, wherein the convergence of the whole algorithm is affected by the selection of a random operator (comprising the cross probability Pc and the variation probability Pm), wherein the Pc takes a value of 0.5, the Pm takes a variable value in the algorithm process, the Pm takes a larger value of 0.05 in the early stage (before 50 generations) of the algorithm, the search space is enlarged, and the Pm takes a smaller value of 0.005 in the later stage (after 50 generations) of the algorithm, so that the convergence speed is accelerated.
Data input in the invention: measuring extinction coefficient of same aerosol particle dispersion system by using laser of different wavelengths of laser radar system
Eliminating unknown parameters from the objective function, the complex refractive index of a given particle +.>
Then->
Only->
So that only +.>
And searching a global optimal solution by using an improved genetic algorithm through assuming a particle distribution model to finally obtain a real particle distribution model. It is assumed that the particle size distribution of a certain aerosol particle group satisfies the normal distribution, as shown in fig. 3. According to the data measured by the multi-wavelength aerosol laser radar, the particle size distribution of the particle swarm is inverted by an extinction method according to a hypothetical distribution model, the particle size distribution obtained by the traditional method is shown in fig. 4, the distribution trend of the particle size distribution approximately accords with the hypothetical model, the particle size distribution diagram obtained by the method is shown in fig. 5, the fitting degree of the distribution trend and the hypothetical model is better, the particle size distribution diagram is smoother, the anti-noise performance of the method is obviously superior to that of the traditional method, and the global optimal solution of the particle size distribution is easier to obtain.
The invention uses genetic algorithm to find the individual which makes the objective function reach the optimal solution by judging the fitness function, then obtains the probability of the corresponding particle size range, thereby determining the particle size distribution of the particles. The genetic algorithm is applied to the inversion problem of particle size in particle size measurement, so that the problems that the traditional inversion algorithm depends on a plurality of priori information, local optimization is easy to fall into during searching and calculating are solved.
The above embodiments are only for illustrating the technical aspects of the present invention, not for limiting the same, and although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may be modified or some or all of the technical features may be replaced with other technical solutions, which do not depart from the scope of the technical solutions of the embodiments of the present invention.
Claims (2)
1. An aerosol particle size inversion method based on a laser radar is characterized by comprising the following steps:
s1, solving a Fredholm first-class integral equation of particle size distribution, wherein the Fredholm first-class integral equation is as follows:
s2 for hypothesis
Performing genetic coding, randomly generating a group of initial strings, and determining the number of initial populationsMGenerating a random number for each cycle, and operating the initial string obtained in the previous time, and reserving the string meeting the requirements to be added into the initial population until the number of the initial population is reached;
s3, establishing an objective function according to a mathematical model:
where n is the combined value of the number of wavelengths of the multi-wavelength lidar system,
optimizing a mathematical model by utilizing an objective function, wherein the optimized decision variable is as follows
And
the constraint is thata<D<b，k>0；
S4, coding by using a floating point number method, and randomly generating a floating point number between 0 and 1 as a gene valued；
S5, determining an individual evaluation method, reversely coding and converting the chromosome strings into true values, mapping the true values to a variable value space, and then obtaining the gene valuesdThe corresponding independent variable real number isd*(b-a)-b；
S6, carrying out population fitness evaluation calculation to ensure that the value of a fitness function is greater than or equal to zero, the minimum value of an objective function corresponds to the maximum value of the fitness function, and taking the fitness function as Fit (f (x))=1/[ 1+c+f (x) ], wherein c=0 is a conservative estimated value of the minimum limit of the objective function, f (x) is an objective function value of a certain point in a solution space, the objective function established by corresponding to S3, and Fit (f (x)) is a fitness function value of a corresponding individual;
s7, designing a genetic operator and determining operation parameters of the genetic algorithm;
s8, completing a first generation operation flow of a genetic algorithm, evaluating the fitness of individuals of a new generation, leaving the father of the new generation and meeting the fitness requirement to enter the next generation, repeating the evolution process, searching the global optimal value of the particle size distribution function, further obtaining the probability of the corresponding particle size range, and determining the particle size distribution of aerosol particles.
2. The method of claim 1, wherein S7 comprises:
s7.1, selecting operation uses a random competition selection operator, in random competition selection, selecting a pair of individuals according to a roulette selection mechanism each time, calculating the proportion of the fitness value of each individual to the fitness value of the individuals in the whole population, enabling the pair of individuals to compete, selecting the individuals with high fitness, and repeating the steps until the selection is full;
s7.2, performing cross operation by using a single-point cross operator, pairing individuals pairwise, randomly setting a cross point in an individual code string for each paired individual, and exchanging partial chromosomes of two paired individuals at the cross point according to the set cross probability so as to generate two new individuals;
s7.3, using a prime mutation operator, assigning each locus of an individual a mutation probability as a mutation point, and replacing each assigned mutation point with other allele values to generate a new generation of individuals.
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