Particle granularity inversion method and device based on improved quantum particle swarm optimization

Abstract

The invention discloses a particle size inversion method and device based on an improved quantum particle swarm algorithm, relates to the technical field of laser particle size measurement, and is implemented based on a small-angle forward scattering method particle size measurement device, initializes a particle swarm by using a reverse learning strategy, and combines the optimization characteristics of the quantum particle swarm algorithm in multiple types of functions to obtain a particle size inversion result. A strategy for position updating by means of selection probability is provided, and a random position is adopted to replace the average optimal position of the current particles, so that the precision of the quantum particle swarm optimization in particle size inversion, especially multi-peak inversion optimization is improved; and after each iteration, better particle position updating is carried out by means of a greedy principle, rapid inversion can be realized for the particle system of which the particle size distribution conforms to various functions, and the method has the advantage of accurately and rapidly inverting the particle size distribution.

Description

Technical Field

[0001] The present invention belongs to the technical field of laser particle size measurement, and particularly relates to a particle size inversion method and device based on an improved quantum particle swarm optimization algorithm. Background Art

[0002] The particle size distribution is an important parameter for evaluating the performance of particles, and its accurate measurement is of great significance for the development of fields such as materials, energy, medicine, chemical engineering, and aerospace. Among various measurement methods for particle size distribution, the particle size measurement technology based on forward small-angle laser diffraction has received extensive attention due to its advantages such as fast measurement speed, high accuracy, wide applicability, and easy implementation of on-line measurement.

[0003] The brief principle of the forward small-angle laser diffraction measurement technology is as follows: A laser beam after beam expansion and collimation interacts with a particle sample, and the spatial distribution of the forward scattered light generated is related to the particle size. The larger the particle size, the more concentrated the forward scattered light distribution. By using an array photodetector to collect the spatial distribution of the forward scattered light, the distribution information of the particle size to be measured can be inversely calculated. Among them, the problem of inversely calculating the particle size distribution based on the spatial distribution of scattered light energy belongs to the first kind of Fredholm integral problem, and it is difficult to give an analytical solution, and an optimization inversion method needs to be used to solve the best approximate solution. Due to the influence of optical noise, electrical noise, etc. widely existing in the measurement environment, the detected scattered light energy distribution signal is disturbed to varying degrees. How to reduce the noise of the measurement system and accurately and quickly invert the particle size is the key problem of the particle size measurement technology by the small-angle forward scattering method.

[0004] The inversion methods for measuring the particle size by the small-angle forward scattering method are generally divided into two types: the independent mode algorithm and the non-independent mode algorithm. Among them, the non-independent mode algorithm needs to know the particle size information of the measured particle system, usually referring to the particle size distribution in the known particle system matching a fixed function relationship expression, and then solving on this mathematical model. Through the optimization algorithm, the parameter value that meets the conditions, that is, the result error is the smallest, can be found, so as to determine the particle size distribution.

[0005] Some non-independent mode methods, such as the pattern search method, the artificial bee colony algorithm ([1] Shan Liang, Li Haoran, Hong Bo, et al. Inversion of multi-peak particle size distribution based on artificial bee colony algorithm [J]. Acta Photonica Sinica, 2020, 49(12): 197-210.), the basic particle swarm optimization algorithm ([2] Cao Lixia, Zhao Jun, Shan Liang, et al. Research on laser particle size detection based on quantum particle swarm optimization algorithm [J]. Applied Laser, 2015, 35(03): 380-386.), etc., all play a certain role in dealing with the problem of particle size inversion, but there are also different limitations: ① For multi-peak distribution particle groups, more parameters need to be searched, which not only increases the computational complexity of inversion, but also results in a low inversion accuracy of particle size distribution; ② Although non-independent mode methods have good anti-noise performance, especially by adopting various improved optimization methods, the robustness of the algorithm is improved to a certain extent ([3] Zhang Biao, Li Shu, Xu Chuanlong, et al. Inversion algorithm of particle size distribution based on RQPSO [J]. Journal of Central South University (Science and Technology), 2016, 47(11): 3922-3928.), but the inversion accuracy drops rapidly in the case of large noise. Summary of the Invention

[0006] In order to solve the problems existing in the above-mentioned prior art, the purpose of the present invention is to provide a particle size inversion method and device based on an improved quantum particle swarm optimization algorithm, which effectively improves the inversion accuracy of multi-peak distribution particle systems, helps to suppress the influence of noise, improves the inversion efficiency and the robustness of the algorithm, and realizes high-precision and stable measurement of particle size distribution.

[0007] In order to achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0008] A particle size inversion method based on an improved quantum particle swarm optimization algorithm is implemented based on a particle size measurement device using the small-angle forward scattering method. The particle swarm is initialized by using a reverse learning strategy, and a position update strategy with a selection probability and a random position is used, combined with the optimization characteristics of the quantum particle swarm optimization algorithm in various functions; after each iteration, the position of a better particle is replaced by means of the greedy principle, and the particle size distribution of particle systems whose particle size distributions conform to various functions is quickly and highly accurately inverted.

[0009] A particle size inversion method based on an improved quantum particle swarm optimization algorithm includes the following steps:

[0010] 1) Select a multi-element photodetector, which is composed of M concentric semi-circular rings or fan-shaped ring arrays, or a planar charge-coupled device, and divide the light intensity into M levels;

[0011] 2) Calculate the light energy distribution coefficient matrix T for measuring the particle size distribution by the small angle forward scattering method. The light energy distribution coefficient matrix T is a matrix of size M×K, where K is the total number of particle size bins:

[0012]

[0013] Among them, the element t in the i-th row and the n-th column i,n The calculation formula is:

[0014]

[0015] t i,n The physical meaning of is the light energy of the diffraction scattered light generated by particles with a diameter of D per unit weight falling on the n-th ring of the multi-element photodetector, J i (), J 0 () are the zero-order Bessel function and the first-order Bessel function respectively; X 1 =πD i,n,1 S i / λf, X n,1 =πD i,n,2 S i / λf; where S n,2 、S n,1 、S n,2 (n = 1, 2....) are the inner and outer radius vectors of each ring, also known as the radial dimension, f is the focal length of the lens, and λ is the wavelength of the light source;

[0016] 3) According to the prior correlation information of the particle system, select the particle size distribution function model f(D|μ,σ) of the particle system;

[0017] 4) Solve the light energy distribution column vector E according to the vector product of the size distribution column vector W and the light energy distribution coefficient matrix T c :

[0018] E c =T*W

[0019] In the formula, the size distribution column vector W is also called the particle weight frequency distribution and can be determined according to the obtained parameters:

[0020] W=(W 1 , W 2 ,…, W j ,…, W K ) T

[0021] Among them, W j =f(D j |μ,σ), D j is the average diameter of the particles in the j-th bin of the particle size bins, K is the total number of particle size bins, and μ and σ are the mean and standard deviation parameters of the particle system;

[0022] 5) Define the objective function of the inversion problem as the calculated value $\mathbf{e}$ of the light energy distribution column vector cal_n and the measured value $\mathbf{e}$ mea_n The residual between them is:

[0023]

[0024] where $F$ is the objective function;

[0025] Before calculating the objective function, normalize the calculated value $\mathbf{e}$ cal_n and the measured value $\mathbf{e}$ mea_n That is,

[0026]

[0027] Use the overall error of the particle weight frequency distribution curve, i.e., the relative root mean square error RRMSE, to evaluate the overall inversion result, and define the error RRMSE algorithm:

[0028]

[0029] In the formula, $W$ set $(D$ j ) = $f(D$ j |$\mu$ set , $\sigma$ set ) is the theoretical weight frequency distribution, $W$ inv $(D$ j ) = $f(D$ j |$\mu$ inv , $\sigma$ inv ) is the weight frequency distribution obtained by inversion, $D$ j is the average diameter of the particles in the $j$-th bin of the particle size bins, $K$ is the total number of particle size bins, $\mu$ set , $\sigma$ set , $\mu$ inv , $\sigma$ inv are the theoretical mean, standard deviation parameters, and the mean and standard deviation parameters obtained by inversion, respectively;

[0030] 6) Based on the improved quantum particle swarm optimization algorithm, find the distribution parameters:

[0031] Define the problem and method parameters: The objective function CostFunction is the objective function defined in step 5); the value ranges of the distribution parameters are set as [Min, Max], where Min and Max are matrices with the lower and upper limits of each distribution parameter in step 3) as elements, and the matrix size is Size; the method parameters include: the number of particles in the particle swarm nPop, the expected precision Precision, and the maximum number of iterations MaxIt. The maximum number of iterations MaxIt and the number of particles in the particle swarm nPop are changed differently according to requirements, and their values are increased to improve the inversion accuracy on the premise of ensuring time.

[0032] Initialization of the particle swarm: The position parameter matrix Position and the objective function value Cost of each particle are stored in a structure of size nPop×1. Pop(i).Cost and Pop(i).Position are the objective function value and the position parameter obtained by the i-th particle respectively; the initialization of the particle positions is completed using the opposition-based learning strategy.

[0033] Subsequently, the initial objective function value is calculated, and the formula is as follows:

[0034] Pop(i).Cost = CostFunction(Pop(i).Position)

[0035] Iteratively optimize the position parameter matrix. Each time an iteration is performed, according to the greedy principle, compare the objective function value of the new particle new with the current particle Pop(i), and keep the particle with a smaller error, that is, a smaller objective function value, for the next iteration. Then compare the objective function value of the retained particle with the historical best particle in the particle swarm to update the position of the historical best particle in the particle swarm best.Position; when the number of iterations of the algorithm reaches the maximum or the objective function value carried by the best particle in the particle swarm reaches the expected precision Precision, it can be determined that the end condition is met and the iteration terminates. At this time, the parameter matrix best carried by the particle with the smallest objective function value is the best distribution parameter found by the improved quantum particle swarm optimization algorithm.

[0036] The formula for step 1) is:

[0037]

[0038] In the formula, i = (1, 2,..., M), S i represents the radial dimension of the i-th ring, D i represents the diameter of the particle, f is the focal length of the lens, and λ is the wavelength of the light source. According to this formula, the upper and lower limits of the particle size that can be measured in actual measurement are calculated.

[0039] In step 3), the particle size distribution function is an arbitrary form of distribution limiting function, including:

[0040] (i) Normal distribution probability density function:

[0041]

[0042] (ii) Rosin-Rammler distribution probability density function:

[0043]

[0044] (iii) Johnson S B distribution function:

[0045]

[0046] where D is the particle size vector, D max , D min , μ, and σ are the maximum and minimum particle sizes, the mean parameter, and the standard deviation parameter, respectively.

[0047] In step 6), according to the formula P forward = L value + r 1 ·(U value - L value ) to generate the position P forward of the solution of the initial particle swarm, and then according to the formula P reverse = r 2 ·(U value + L value ) - P forward to generate the reverse particle swarm P reverse of the initial particle swarm; merge P forward and P reverse to form a new particle swarm, and select the first N particles according to the value of Cost as the initial particle swarm solution of the improved quantum particle swarm algorithm after final initialization; where N is nPop, i.e., the number of particles in the particle swarm, U value and L value are the upper and lower limits of each parameter of the particles matching the number of particles nPop in the particle swarm, r 1 and r 2 are uniformly distributed random numbers in the range (0, 1) matching L value and U value .

[0048] In step 6), the iterative optimization of the position parameter matrix is specifically as follows:

[0049] According to the value of p 1 , that is, the probability value, to determine the different movement processes of the particles, p 1is a random number uniformly distributed between (0,1). If p 1 ≤ 0.5, the position update formula is:

[0050] new.Position = Pop(k 1 ).Position + phi * (Pop(k 1 ).Position - Pop(i).Position)

[0051] where the parameter phi is a random number uniformly distributed with boundaries -1 and 1, Pop(i) is the current particle, and k 1 is a random integer in the range [1, nPop] other than i, and Pop(k 1 ) is a random particle other than the current particle;

[0052] If p 1 > 0.5, the position update formula is:

[0053]

[0054] In the formula, q i and L i are respectively:

[0055]

[0056] L i = 2·α|p m - Pop(i).Position|

[0057] p m = Pop(k 2 ).Position

[0058] In the formula, C 1 and C 2 are acceleration coefficients, both taking 1.5, p g is the historical best particle position of the particle swarm, that is, best.Position; α is the attraction and diffusion coefficient, α = 0.7 - 0.4 * It / MaxIt, where It is the current iteration number; R, R 1 and R 2 are all random number matrices uniformly distributed in the interval [0,1]; k 2 is a random integer in the range [1, nPop] other than i. Here, the Pop(k m ).Position taken by p 2 is the position of a random particle other than the current particle.

[0059] In step 6), the particle swarm particle number nPop is used to control the maximum number of active particles in the method, and the expected precision Precision and the maximum number of iterations MaxIt are used to control when the iteration ends. The parameters of the improved quantum particle swarm algorithm for the multi-peak mixed distribution parameter inversion problem can be determined by performing parameter optimization experiments.

[0060] The invention discloses a device for realizing a particle size inversion method based on an improved quantum particle swarm algorithm, comprising a particle size measuring device using a small-angle forward scattering method, wherein the particle size measuring device using a small-angle forward scattering method comprises a laser 1, a first aperture 2, a first lens 3, a spatial filter 4, a second lens 5, a sample area 6 to be measured, a Fourier receiving lens 7 and a multi-element photodetector 8 which are arranged in sequence, wherein the laser 1 uses a visible light laser light source, the first aperture 2 uses a circular aperture, the first lens 3 and the second lens 5 which are placed at the same focal point, and the spatial filter 4 which is placed at the focal position together form a laser beam expansion and collimation system; the sample area 6 to be measured uses a transparent cuvette or a part of a sample circulation system, and the forward diffraction scattered light signal is focused onto the multi-element photodetector 8 placed on a Fourier conjugate plane through the Fourier receiving lens 7.

[0061] A particle size inversion device based on an improved quantum particle swarm algorithm can set values ​​for refractive index and photoelectric detector parameters when measuring particle size distribution parameters, display the small-angle forward scattering measurement results of light energy distribution, background light intensity and particle size distribution, and provide a storage medium that can save relevant parameters and inversion results in the background for users to use.

[0062] The storage medium is a computer program, which is used to be stored in a computer-readable medium and provides a user input interface to implement a particle size inversion method based on an improved quantum particle swarm algorithm.

[0063] Compared with the prior art, the present invention has the following beneficial effects:

[0064] The present invention proposes a particle size inversion method and device based on an improved quantum particle swarm algorithm, which can be used for the inversion of various forms of particle size distribution functions, including but not limited to normal distribution, Rosin-Rammler distribution, Johnson S distribution, etc. B Distribution, etc., and has a wide range of applications.

[0065] In view of the fact that the existing technology is affected by factors such as environmental and system noise and multi-peak particle size distribution, and has problems such as large inversion error and low inversion efficiency, the present invention adopts random positions to replace the average optimal position, proposes a position update strategy based on selection probability, and uses a reverse learning strategy to initialize the particle swarm, thereby effectively improving the inversion accuracy of the algorithm in multi-peak conditions and significantly enhancing the noise resistance. Brief Description of the Drawings

[0066] Figure 1 This is a schematic diagram of a particle size inversion device based on an improved quantum particle swarm optimization algorithm according to an embodiment of the present invention.

[0067] Figure 2 This is a flowchart of a particle size inversion method based on an improved quantum particle swarm optimization algorithm according to an embodiment of the present invention.

[0068] Figure 3 This is a flowchart of an improved quantum particle swarm optimization algorithm according to an embodiment of the present invention.

[0069] Figure 4 This is the inversion results of particle systems with unimodal and bimodal normal distributions of particle size distributions according to embodiments of the present invention under noise-free and noisy conditions; (a), (b) noise intensity 0%; (c), (d) noise intensity 1%; (e), (f) noise intensity 3%; (g), (h) noise intensity 5%.

[0070] Figure 5 This is the inversion results of particle systems with unimodal and bimodal Rosin-Rammler distributions of particle size distributions according to embodiments of the present invention under noise-free and noisy conditions; (a), (b) noise intensity 0%; (c), (d) noise intensity 1%; (e), (f) noise intensity 3%; (g), (h) noise intensity 5%.

[0071] Figure 6 This is for particle systems with unimodal and bimodal Johnson S B distributions of particle size distributions according to embodiments of the present invention under noise-free and noisy conditions; (a), (b) noise intensity 0%; (c), (d) noise intensity 1%; (e), (f) noise intensity 3%; (g), (h) noise intensity 5%.

[0072] Figure 7 This is the inversion results of particle systems with a trimodal normal distribution of particle size distributions according to embodiments of the present invention under noise-free and noisy conditions; (a) noise intensity 0%; (b) noise intensity 1%; (c) noise intensity 3%; (d) noise intensity 5%. Detailed Description of the Invention

[0073] The present invention will be described in detail below with reference to the embodiments and the drawings.

[0074] Refer to Figure 1A particle size inversion device based on an improved quantum particle swarm algorithm includes a small-angle forward scattering method particle size measuring device, which includes a laser 1, a first aperture 2, a first lens 3, a spatial filter 4, a second lens 5, a sample area 6 to be measured, a Fourier receiving lens 7 and a multi-element photodetector 8 arranged in sequence, wherein the laser 1 uses a visible light laser light source, the first aperture 2 uses a circular aperture, the first lens 3 and the second lens 5 placed at the same focal point, together with the spatial filter 4 placed at the focal position, form a laser beam expansion and collimation system; the sample area 6 to be measured uses a transparent cuvette or a part of a sample circulation system for placing a static suspended sample or a dynamically circulating sample to be measured; the forward diffraction scattered light signal is focused onto a multi-element photodetector 8 placed on a Fourier conjugate plane through a Fourier receiving lens 7, and the multi-element photodetector 8 is a photodetector array for receiving diffraction scattered light intensity, which is a multi-element ring photodetector or a planar charge coupled device.

[0075] The particle size inversion device based on the improved quantum particle swarm algorithm can set values ​​for refractive index, photoelectric detector parameters, etc. when measuring parameters of particle size distribution, display small-angle forward scattering measurement results such as light energy distribution, background light intensity and particle size distribution, and provide a storage medium that can save relevant parameters and inversion results in the background for users to use.

[0076] The storage medium is a computer program that can be stored in a computer-readable medium and provides a user input interface to implement a particle size inversion method based on an improved quantum particle swarm algorithm.

[0077] A particle size inversion method based on an improved quantum particle swarm algorithm using the device is proposed. A reverse learning strategy is used to initialize the particle swarm, and a position update strategy with the help of selection probability is proposed, and a random position is used to replace the current average optimal position of the particle. Combined with the optimization characteristics of the quantum particle swarm algorithm in multiple types of functions, the accuracy of the quantum particle swarm algorithm in the inversion optimization process is improved, and the time required for inversion is reduced. After each iteration, a better particle position is replaced with the help of the greedy principle, so that the particle size distribution of the particle system whose particle size distribution conforms to various functions is quickly and accurately inverted.

[0078] Reference Figure 2 , a particle size inversion method based on an improved quantum particle swarm algorithm, comprising the following steps:

[0079] 1) A multi-element annular photodetector is selected as the multi-element photodetector 8. The multi-element photodetector 8 is composed of M=31 concentric semicircular rings, that is, a total of M=31 rings are divided; the ring division formula is:

[0080]

[0081] In the formula, i = (1, 2, …, M), S i represents the radial dimension of the i-th ring, D i represents the diameter of the particle, f is the focal length of the lens, λ is the wavelength of the light source, and the upper and lower limits of the particle size that can be measured in actual measurement are calculated according to this formula;

[0082] The dimensions of each ring of the multi-element photodetector 8 in this embodiment are shown in Table 1;

[0083] Table 1 Dimension parameters of each ring of the multi-element photodetector

[0084]

[0085]

[0086] 2) Calculate the light energy distribution coefficient matrix T for measuring the particle size distribution by the small-angle forward scattering method. The light energy distribution coefficient matrix T is a matrix of size M×K, where K is the total number of particle size bins:

[0087]

[0088] Among them, the element t in the i-th row and the n-th column i,n The calculation formula is:

[0089]

[0090] t i,n The physical meaning of is the light energy of the diffracted light generated by particles with a diameter of D per unit weight i falling on the n-th ring of the multi-element photodetector, J 0 (), J 1 () are the zero-order Bessel function and the first-order Bessel function respectively; X i,n,1 = πD i S n,1 / λf, X i,n,2 = πD i S n,2 / λf; where S n,1 , S n,2 (n = 1, 2....) are the inner and outer radius vectors of each ring, also called the radial dimension, λ is the wavelength of the light source, and f is the focal length of the lens; in this embodiment, λ = 632.8 nm and f = 0.3 m are set;

[0091] 3) According to the relevant information of the particle system, select the particle size distribution function model f(D|μ, v) of the particle system; the particle size distribution function is a distribution limiting function in any form, including but not limited to:

[0092] (i) Normal distribution probability density function:

[0093]

[0094] (ii) Rosin-Rammler distribution probability density function:

[0095]

[0096] (iii) Johnson S B distribution function:

[0097]

[0098] where D is the particle size vector, and D max , D min , μ, and σ are the maximum and minimum particle sizes, the mean parameter, and the standard deviation parameter, respectively;

[0099] 4) Solve for the light energy distribution column vector E based on the vector product of the size distribution column vector W and the light energy distribution coefficient matrix T c :

[0100] E c = T * W

[0101] In the formula, the size distribution column vector W is also called the particle weight frequency distribution and can be determined based on the obtained parameters:

[0102] W = (W 1 , W 2 , …, W j , …, W K ) T

[0103] where W j = f(D j |μ, σ), D j is the average diameter of the particles in the j-th size bin, K is the total number of size bins, and μ and σ are the mean and standard deviation parameters of the particle system;

[0104] 5) Define the objective function of the inversion problem as the residual between the calculated value e cal_n of the light energy distribution column vector and the measured value e mea_n :

[0105]

[0106] where F is the objective function and M is the total number of rings of the multi-element photodetector;

[0107] Before actually calculating the objective function, first normalize the calculated value e cal_n and the measured value e mea_n , that is

[0108]

[0109]

[0110] The overall error of the particle weight frequency distribution curve, i.e., the relative root mean square error RRMSE, is used to comprehensively evaluate the inversion results, and the error RRMSE algorithm is defined as follows:

[0111]

[0112] where W set (D j ) = f(D j |μ set , σ set ) is the theoretical weight frequency distribution, W inv (D j ) = f(D j |μ inv , σ inv ) is the weight frequency distribution obtained by inversion, D j is the average diameter of the particles in the j-th bin of the particle size bins, K is the total number of particle size bins, μ set , σ set , μ inv , σ inv are the theoretical mean, standard deviation parameters, and the mean and standard deviation parameters obtained by inversion, respectively;

[0113] 6) Refer to Figure 3 to find the distribution parameters based on the improved quantum particle swarm optimization algorithm;

[0114] Define the parameters related to the problem and the inversion method: The objective function CostFunction is the objective function determined in step 5); the value range of the distribution parameters is set as [Min, Max], where Min and Max are matrices with the lower and upper boundary values of each distribution parameter in step 3) as elements. Taking the bimodal normal distribution as an example, set Min = [3, 0, 0; 3, 0, 0], Max = [100, 20, 1; 100, 20, 1], and the size of the two matrices is Size, Size = [2, 3]; the method parameters include: the maximum number of iterations MaxIt = 500, the number of particles in the particle swarm nPop = 400, and the expected accuracy Precision = 1E-30;

[0115] Initialization of the particle swarm: The position parameter matrix Position and the objective function value Cost of each particle are stored in a structure of size nPop×1. Pop(i).Cost and Pop(i).Position are the objective function value and the position parameter obtained by the i-th particle, respectively; the initialization of the particle position is completed using the reverse learning strategy.

[0116] According to the formula P forward = L value + r 1 ·(U value - L value ) to generate the position P of the solution of the initial particle swarm forward , and then according to the formula P reverse = r 2 ·(U value + L value ) - P forward to generate the reverse particle swarm P reverse of the initial particle swarm; Combine P forward and P reverse to form a new particle swarm, and select the first N particles according to the value of Cost as the initial particle swarm solution for improving the quantum particle swarm optimization algorithm after final initialization; where N is nPop, that is, the number of particles in the particle swarm, U value and L value are the upper and lower limits of each particle parameter that match the number of particles nPop in the particle swarm respectively, r 1 and r 2 are uniformly distributed random numbers within the range (0, 1) that match L value and U value ;

[0117] Then calculate the initial objective function value, and its formula is:

[0118] Pop(i).Cost = CostFunction(Pop(i).Position)

[0119] Iteratively optimize the position parameter matrix, and the whole iterative process is:

[0120] According to p 1 , that is, the value of probability, to determine the different movement processes of the particles. p 1 is a uniformly distributed random number between (0, 1). If p 1 ≤0.5, then the position update formula is:

[0121] new.Position = Pop(k 1 ).Position + phi * (Pop(k 1 ).Position - Pop(i).Position)

[0122] Among them, the parameter phi is a uniformly distributed random number and is bounded by -1 and 1. Pop(i) is the current particle, k 1 is a random integer within the range [1, nPop] except i, Pop(k 1is a random particle other than the current particle. This step is to determine the local search range based on the current particle and the random particle;

[0123] If p 1 > 0.5, the position update formula is:

[0124]

[0125] In the formula, q i and L i are respectively:

[0126]

[0127] L i = 2·α|p m - Pop(i).Position|

[0128] p m = Pop(k 2 ).Position

[0129] In the formula, C 1 and C 2 are acceleration coefficients, both taken as 1.5 here. p g is the historical best particle position of the particle swarm, that is, best.Position; α is the attraction and diffusion coefficient, α = 0.7 - 0.4*It / MaxIt, where It is the current iteration number; R, R 1 and R 2 are all random number matrices uniformly distributed in the range [0, 1]; k 2 is a random integer other than i in the range [1, nPop]. Here, the Pop(k m ).Position taken by p 2 is the position of a random particle other than the current particle, used to replace the average optimal particle position generally used in the algorithm;

[0130] Each time an iteration is performed, according to the greedy principle, compare the objective function values of the new particle new and the current particle Pop(i), and keep the particle with a smaller error, that is, the particle with a smaller objective function value, for the next iteration. Then compare the retained particle with the historical best particle of the particle swarm in terms of the objective function value to update the position of the historical best particle position best.Position of the particle swarm. When the iteration number of the algorithm reaches the maximum or the objective function value carried by the best particle of the particle swarm reaches the expected accuracy Precision, that is, the preset end condition is reached and the iteration terminates. At this time, the parameter matrix best carried by the particle with the smallest objective function value is the best distribution parameter found by the improved quantum particle swarm optimization algorithm.

[0131] Refer to Figure 4, Figure 4 The inversion results of the particle systems with unimodal and bimodal normal distribution of particle sizes in this embodiment under noise-free and noisy conditions; (a), (b) noise intensity 0%; (c), (d) noise intensity 1%; (e), (f) noise intensity 3%; (g), (h) noise intensity 5%; It can be seen from Figure 4 that adding noise will cause minor local changes in the inversion distribution, but the overall effect is good. Table 2 lists the inversion result data, where Pe in the table is the proportion of each peak. It can be seen from Table 2 that the error of the result under noise-free conditions is zero, and the inversion effect is excellent; although the error will gradually increase with the increase of noise, the error magnitudes of the inversion results are within the engineering acceptable error range, proving that the method of this embodiment has good noise resistance and high robustness; at the same time, the inversion time for both unimodal and bimodal is short, proving that this method can perform fast inversion.

[0132] Table 2 Inversion results of unimodal and bimodal normal distribution particle systems under noise-free and noisy conditions of scattered light energy distribution

[0133]

[0134] Refer to Figure 5 , Figure 5 This is the comparison of the theoretical and inversion results after adding different degrees of noise to the light energy signals conforming to unimodal and bimodal Rosin-Rammler distributions in this embodiment; (a), (b) noise intensity 0%; (c), (d) noise intensity 1%; (e), (f) noise intensity 3%; (g), (h) noise intensity 5%; It can be seen from Figure 5 that adding noise will cause minor local changes in the inversion distribution, but the overall effect is good. Table 3 lists the result data of the distribution inversion. It can be seen from the table that although the error will gradually increase with the increase of noise, the error magnitudes of the inversion results are within the engineering acceptable error range, proving that the method of this embodiment has good noise resistance and high robustness.

[0135] Table 3 Inversion results of unimodal and bimodal Rosin-Rammler distribution particle systems under noise-free and noisy conditions of scattered light energy

[0136]

[0137]

[0138] Refer to Figure 6 , Figure 6 This is for this embodiment to conform to unimodal and bimodal Johnson S BComparison of theoretical and inversion results after adding different intensities of noise to the distributed light energy signal; (a), (b) noise intensity 0%; (c), (d) noise intensity 1%; (e), (f) noise intensity 3%; (g), (h) noise intensity 5%; From Figure 6 it can be seen that the overall effect is very good. Table 4 lists the result data of the distribution inversion. From Table 4, it can be seen that the method of this embodiment has good noise resistance and high robustness.

[0139] Table 4 Inversion results of single- and double-peak JohnsonS B distribution particle system under noise-free and noisy scattered light energy

[0140]

[0141] Refer to Figure 7 , Figure 7 This is the comparison of theoretical and inversion results after adding different intensities of noise to the light energy signal that conforms to the three-peak normal distribution in this embodiment; (a) noise intensity 0%; (b) noise intensity 1%; (c) noise intensity 3%; (d) noise intensity 5%; Table 5 lists the result data of the distribution inversion; From Figure 7 it and Table 5, it can be seen that as the noise increases, the accuracy will decrease. Especially when 5% random noise is loaded, the error reaches more than 10%. However, in terms of the three-peak accuracy, it is acceptable and has good noise resistance.

[0142] Table 5 Inversion results of three-peak normal distribution particle system under noise-free and noisy scattered light energy

[0143]

Claims

1. A particle size inversion method based on an improved quantum particle swarm algorithm, implemented based on a small-angle forward scattering particle size measurement device, characterized in that: include: The particle swarm is initialized by using the reverse learning strategy, and the position update strategy with the selection probability is adopted with random positions, combined with the optimization characteristics of the quantum particle swarm algorithm in multiple types of functions. After each iteration, the greedy principle is used to replace the particle position with a better particle position, and the particle size distribution of the particle system that conforms to various functions is quickly and accurately inverted.

2. The method according to claim 1, characterized in that The following steps are involved: 1) Select a multi-element photodetector, which is composed of M concentric semicircular rings or fan-shaped rings in an array, or a planar charge-coupled device, and divides the light intensity into M levels; 2) Calculate the light energy distribution coefficient matrix T for measuring particle size distribution using the small-angle forward scattering method. The light energy distribution coefficient matrix T is a matrix of size M×K, where K is the total number of particle size bins: The element t in row i and column n is i,n The calculation formula is: t i,n The physical meaning is that the diameter per unit weight is D i The diffraction scattered light generated by the particles falls on the nth ring of the multi-element photodetector. J0() and J1() are the zero-order Bessel function and the first-order Bessel function respectively; X i,n,1 =πD i S n,1 / λf,X i,n,2 =πD i S n,2 / λf; where S n,1 , S n,2 (n=1,2....) is the inner and outer radius vector of each ring, also called radial dimension, f is the focal length of the lens, and λ is the wavelength of the light source; 3) According to the prior information of the particle system, select the particle size distribution function model f(D|μ,σ); 4) Solve the light energy distribution column vector E based on the vector product of the size distribution column vector W and the light energy distribution coefficient matrix T c : E c =T*W In the formula, the size distribution column vector W is also called the particle weight frequency distribution, which is determined according to the obtained parameters: In=(In1,In2,…,In j ,…,IN K ) T Among them, W j =f(D j |μ,σ),D j is the average diameter of particles in the jth particle size classification, K is the total number of particle size classifications, μ and σ are the mean and standard deviation parameters of the particle system; 5) Define the objective function of the inversion problem as the calculated value of the light energy distribution column vector e cal_n With the measured value e mea_n The residual between: Where F is the objective function; Before calculating the objective function, we first calculate the value e cal_n and the measured value e mea_n Normalized, that is The overall error of the particle weight frequency distribution curve, namely the relative root mean square error (RRMSE), is used to evaluate the inversion results as a whole, and the error RRMSE algorithm is defined as follows: Where W set (D j )=f(D j |μ set ,σ set ) is the theoretical weight frequency distribution, W inv (D j )=f(D j |μ inv ,σ inv ) is the weight frequency distribution obtained by inversion, D j is the average diameter of the particles in the jth particle size classification, K is the total number of particle size classifications, μ set , σ set , μ inv , σ inv are the theoretical mean and standard deviation parameters and the mean and standard deviation parameters obtained by inversion; 6) Finding distribution parameters based on improved quantum particle swarm algorithm: Define the problem and method parameters: the objective function CostFunction is the objective function defined in step 5); the range of each distribution parameter is set to [Min, Max], Min and Max are the lower and upper boundary values ​​of each distribution parameter in step 3), and the matrix is ​​Size; the method parameters include: the number of particles in the particle swarm nPop, the expected precision Precision and the maximum number of iterations MaxIt. The maximum number of iterations MaxIt and the number of particles in the particle swarm nPop are changed according to different requirements. The inversion accuracy can be increased by increasing the values ​​of the two while ensuring the time. Particle swarm initialization: The position parameter matrix Position and the objective function value Cost of each particle are stored in a structure of size nPop×1. Pop(i).Cost and Pop(i).Position are the objective function value and position parameter obtained by the i-th particle respectively. The reverse learning strategy is used to initialize the particle position: Calculate the initial objective function value, the formula is as follows: Pop(i).Cost=CostFunction(Pop(i).Position) The position parameter matrix is ​​optimized iteratively. Each time iterates, according to the greedy principle, the objective function value of the new particle new is compared with that of the current particle Pop(i). The particle with smaller error, i.e. smaller objective function value, is retained for the next iteration and the objective function value of the retained particle is compared with that of the best particle in the history of the particle swarm to update the position of the best particle in the history of the particle swarm, best.Position. When the number of iterations reaches the maximum or the objective function value carried by the best particle in the particle swarm reaches the expected precision, it can be determined that the end condition is met and the iteration terminates. At this time, the parameter matrix best carried by the particle with the smallest objective function value is the best distribution parameter found by the improved quantum particle swarm algorithm.

3. The method according to claim 2, characterized in that Step 1) The ring division formula is: Where i = (1, 2, ..., M), S i Denotes the radial dimension of the ith ring, D i represents the diameter of the particle, f is the focal length of the lens, and λ is the wavelength of the light source. The upper and lower limits of the particle size that can be measured in actual measurement are calculated based on this formula.

4. The method according to claim 2, characterized in that: In step 3), the particle size distribution function is a distribution-limiting function in any form, including: (i) Normal distribution probability density function: (ii) Rosin-Rammler distribution probability density function: (iii) Johnson S B Distribution function: Where D is the particle radial dimension, D max , D min , μ, σ are the maximum and minimum particle sizes, mean parameters and standard deviation parameters respectively.

5. The method according to claim 2, characterized in that: Step 6) According to the formula P forward =L value +r1·(U value -L value ) Generate the position P of the solution of the initial particle swarm forwaed , and then according to the formula P reverse = r2·(U value +L value )-P forward Generate the reverse particle swarm P of the initial particle swarm reverse ; forward and P reverse The two are merged to form a new particle swarm, and the first N particles are selected according to the value of Cost as the initial particle swarm solution of the improved quantum particle swarm algorithm after final initialization; where N is nPop, i.e. the number of particles in the particle swarm, and U is value With L value They are the upper and lower limits of the particle parameters that match the particle swarm number nPop, r1 and r2 are the value with U value Matches a uniformly distributed random number in the range (0,1).

6. The method according to claim 5, characterized in that The iterative optimization of the position parameter matrix in step 6) is specifically as follows: The different movement processes of the particle are determined according to the value of p1, which is the probability. p1 is a random number uniformly distributed between (0,1). If p1≤0.5, the position update formula is: new.Position=Pop(k1).Position+phi*(Pop(k1).Position-Pop(i).Position) Wherein, parameter phi is a uniformly distributed random number with -1 and 1 as the boundary, Pop(i) is the current particle, k1 is a random integer other than i in the range [1, nPop], and Pop(k1) is a random particle other than the current particle; If p1>0.5, the position update formula is: In the formula, q i and L i They are: L i 2·α|p m -Pop(i).Position| p m =Pop(k2).Position Where C1 and C2 are acceleration coefficients, both are 1.5, p g is the best particle position in the history of the particle swarm, that is, best.Position; α is the attraction diffusion coefficient, α = 0.7-0.4*It / MaxIt, where It is the current iteration number; R, R1 and R2 are all random number matrices that obey uniform distribution in the interval [0,1]; k2 is a random integer other than i in the range [1, nPop], where p m The Pop(k2).Position taken is the position of a random particle except the current particle.

7. The method according to claim 2, characterized in that: In step 6), the particle swarm particle number nPop is used to control the maximum number of active particles in the method, the expected precision Precision and the maximum number of iterations MaxIt are used to control when the iteration ends, and the parameters of the improved quantum particle swarm algorithm for the multi-peak mixed distribution parameter inversion problem are determined by performing parameter optimization experiments.

8. A particle size inversion device based on an improved quantum particle swarm algorithm for implementing the method of claim 1, comprising a particle size measurement device using a small-angle forward scattering method, characterized in that: The particle size measuring device using a small-angle forward scattering method comprises a laser (1), a first aperture (2), a first lens (3), a spatial filter (4), a second lens (5), a sample area to be measured (6), a Fourier receiving lens (7) and a multi-element photoelectric detector (8) which are arranged in sequence. The laser (1) uses a visible light laser light source, the first aperture (2) uses a circular aperture, the first lens (3) and the second lens (5) arranged at the same focal point, together with the spatial filter (4) placed at the focal position, form a laser beam expansion and collimation system; the sample area to be measured (6) uses a transparent cuvette or a part of a sample circulation system, and the forward diffraction scattered light signal is focused onto the multi-element photoelectric detector (8) placed on the Fourier conjugate plane through the Fourier receiving lens (7).

9. The device according to claim 8, characterized in that: When measuring the parameters of particle size distribution, the refractive index and photoelectric detector parameters can be set and taken, and the small-angle forward scattering measurement results of light energy distribution, background light intensity and particle size distribution can be displayed. A storage medium is provided to save the relevant parameters and inversion results in the background for users to use.

10. The device according to claim 9, characterized in that: The storage medium is a computer program, which is used to be stored in a computer-readable medium and provides a user input interface to implement a particle size inversion method based on an improved quantum particle swarm algorithm.

Images