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    • 专利摘要:
    A dynamic light scattering inversion method of non-negative TSVD for adaptive sampling of particle size distribution, belonging to the technical field of dynamic light scattering, and comprising the following steps: step 1001. determining initial parameters; step 1002. inverting particle size distribution of particles; steps 1003 - 1004. reconstructing electric field autocorrelation functions, and calculating residuals of the electric field autocorrelation functions; step 1005. increasing the number of particle size distribution sampling points; step 1006. if the number of current particle size distribution sampling points meets a trigger condition, executing step 1007, otherwise, returning to steps 1002 - 1005; step 1007. calculating the minimum value of the residuals of the electric field autocorrelation functions; step 1008. obtaining the optimal sampling point number; and step 1009. obtaining the particle size distribution of the particles corresponding to the optimal sampling point number. Compared with the traditional non-negative TSVD for fixed particle size distribution sampling points, the dynamic light scattering inversion method of non-negative TSVD for adaptive sampling of particle size distribution with higher antiinterference capability has the advantages that the inversion accuracy is improved, and the improvement effect is more obvious under a high noise level.
    公开号:NL2026543A
    申请号:NL2026543
    申请日:2020-09-25
    公开日:2021-05-25
    发明作者:Wang Yajing；Shen Jin；Liu Wei；Chen Wengang；Ma Lixiu；Yuan Xi；Liu Zhenming；Mou Tongtong
    申请人:Univ Shandong Technology；
    IPC主号:
    专利说明:

    DYNAMIC LIGHT SCATTERING INVERSION METHOD OF NON-NEGATIVE TSVD FOR
    ADAPTIVE SAMPLING OF PARTICLE SIZE DISTRIBUTION Technical Field A dynamic light scattering inversion method of non-negative TSVD for adaptive sampling of particle size distribution, belonging to the technical field of dynamic light scattering, Background As a method for quickly and effectively measuring submicron and nanometer particles, dynamic light scattering (hereinafter referred to as DLS) technique is widely used in medicine, chemistry, biology, polymer material and other fields. In the technique, scattered light of random fluctuation is obtained according to the Brownian motion of particles in the suspension, thus obtaining an autocorrelation function (hereinafter referred to as ACF) of light intensity, further, an electric field autocorrelation function is solved according to the Siegert relationship, and then the particle size distribution (hereinafter referred to as PSD) of particles is solved.
    It is a typical ill-posed problem that obtaining the particle size distribution of particles from the scattered light correlation function requires solving the first kind of Fredholm integral equation. In order to obtain accurate PSD, optimization methods based on different principles are proposed one after another, including cumulant analysis method, non-negative constrained least-squares (NNLS) algorithm, CONTIN algorithm, Laplace transform method, exponential sampling method, Tikhonov regularization method, Bayesian algorithm and various intelligent algorithms. The existing methods generally have the following problem: these methods generally use a fixed number of particle size distribution sampling points in the inversion process. However, the selection of particle size distribution sampling points is related to the inversion accuracy. Different particles require different particle size distribution sampling points, and the particle size distribution sampling points required for the same particles under different random noises are also different. Too few particle size distribution sampling points may cause the peak position to deviate greatly from the true value and the smoothness of inversion results to be poor, and too many particle size distribution sampling points may cause the inverted PSD to deviate seriously from the real PSD. Appropriate number of particle size distribution sampling points is beneficial to improving the accuracy of the inverted PSD. Therefore, how to select an appropriate number of particle size distribution sampling points to obtain higher PSD accuracy becomes a problem urgently to be solved in the art.
    Summary In order to solve the technical problem so as to overcome the defects of the prior art, the present invention provides a dynamic light scattering inversion method of non-negative TSVD for adaptive sampling of particle size distribution which has the advantages that the inversion accuracy is improved, the improvement effect is more obvious under a high noise level, and the anti-interference capability is higher as compared with the traditional non-negative TSVD for fixed particle size distribution sampling points.
    A technical solution adopted in the present invention to solve the technical problem is as follows: the dynamic light scattering inversion method of non-negative TSVD for adaptive sampling of particle size distribution, comprising the following steps: step 1001. determining initial parameters; step 1002. inverting particle size distribution of particles adopting the non-negative TSVD regularization principle; step 1003. reconstructing electric field autocorrelation functions, and calculating residuals of the electric field autocorrelation functions with the actually measured electric field ACF; step 1004. saving the residuals of the electric field autocorrelation function calculated in the step 1003; step 1005. increasing the number of particle size distribution sampling points; step 1006. determining whether the current particle size distribution sampling point number meets a trigger condition, if s0, executing step 1007, otherwise, returning to steps 1002-1005; step 1007. calculating the minimum value of the residuals of the electric field autocorrelation functions; step 1008. obtaining the optimal sampling point number corresponding to the minimum value of the residuals of the electric field autocorrelation functions; and step 1009. obtaining the particle size distribution of the particles corresponding to the optimal sampling point number.
    Preferably, the trigger condition in the step 1006 is that: the number of particle size distribution sampling points is greater than the number of correlation function channels.
    Preferably, the initial parameters in the step 1001 are: the initial value of the number s of particle size distribution points: s=30, the step length /: equal to 5.
    Preferably, the expression of the minimum value of the residuals of the electric field autocorrelation functions is: RESmin=min(|g(Ts)-g1(1)|2) where s represents the number of sampling points, g(1s)=AsPSDs represents the reconstructed electric field autocorrelation function, and g:+(T) represents the actually measured electric field autocorrelation function.
    Preferably, in the step 1005, the increase in the number of particle size distribution sampling points is the value of one step length.
    Compared with the prior art, the present invention has the advantageous effects that: The dynamic light scattering inversion method of non-negative TSVD for adaptive sampling of particle size distribution has the advantages that the inversion accuracy is improved, the improvement effect is more obvious under a high noise level, and the anti-interference capability is higher as compared with the traditional non-negative TSVD for fixed particle size distribution sampling points.
    For bimodal distribution, the dynamic light scattering inversion method of non-negative TSVD for adaptive sampling of particle size distribution improves the accuracy of inverted PSD, the relative error and error of peak position of the inversion result thereof are significantly lower than those of the fixed algorithm.
    With the size increase of mixed particles in the bimodal distribution, the deviation between the inverted PSD of the fixed algorithm and the theoretical PSD gradually increases, and the inverted PSD has no bimodal distribution feature under a high noise level; while the inverted PSD of the adaptive algorithm is significantly improved, and has obvious pimodal distribution features under different noise levels.
    Therefore, the dynamic light scattering inversion method of non-negative TSVD for adaptive sampling of particle size distribution has a wide range of application and high anti-noise capability.
    Description of Drawings Fig. 1 is a flow chart showing the dynamic light scattering inversion method of non-negative TSVD for adaptive sampling of particle size distribution.
    Fig. 2 is a curve chart showing the relative error of 387 nm unimodal wide distribution under different particle size distribution sampling points.
    Fig. 3 is a curve chart showing the relative error of 398 nm unimodal narrow distribution under different particle size distribution sampling points.
    Fig. 4 is a curve chart showing the relative error of 170/421 nm bimodal distribution under different particle size distribution sampling points.
    Fig. 5 is a curve chart showing the relative error of 185/666 nm bimodal distribution under different particle size distribution sampling points.
    Fig. 6 is a curve chart showing the relative error of 335/840 nm bimodal distribution under different particle size distribution sampling points.
    Figs. 7-9 are curve charts showing the inverted PSD of 398 nm unimodal narrow distribution when the number of particle size distribution sampling points is 10-150. Figs. 10-12 are curve charts showing the inverted PSD of 170/421 nm bimodal distribution when the number of particle size distribution sampling points is 10-150. Fig. 13 is a curve chart showing the relative error of particle size distribution when the number of particle size distribution sampling points of unimodal narrow distribution is 30-120. Fig. 14 is a curve chart showing the residual of the autocorrelation function when the number of particle size distribution sampling points of unimodal narrow distribution is 30-120. Fig. 15 is a curve chart showing the relative error of particle size distribution when the number of particle size distribution sampling points of bimodal distribution is 30-120. Fig. 16 is a curve chart showing the residual of the autocorrelation function when the number of particle size distribution sampling points of bimodal distribution is 30-120.
    Fig. 17 is a curve chart showing the relative error under different number of sampling points of 398 nm unimodal narrow distribution when the number of channels is 80. Fig. 18 is a curve chart showing the relative error under different number of sampling points of 398 nm unimodal narrow distribution when the number of channels is160. Fig. 19 is a curve chart showing the relative error under different number of sampling points of 398 nm unimodal narrow distribution when the number of channels is 210. Figs. 20-21 are curve charts showing the inverted PSD under different number of sampling points of 398 nm unimodal narrow distribution when the number of channels is 80. Figs. 22-23 are curve charts showing the inverted PSD under different number of sampling points of 398 nm unimodal narrow distribution when the number of channels is 160. Figs. 24-25 are curve charts showing the inverted PSD under different number of sampling points of 398 nm unimodal narrow distribution when the number of channels is 210. Fig. 26 is a curve chart showing the inverted PSD under 170/421 nm bimodal distribution when the noise level is 1*104. Fig. 27 is a curve chart showing the inverted PSD under 170/421 nm bimodal distribution when the noise level is 1*10°3. Fig. 28 is a curve chart showing the inverted PSD under 170/421 nm bimodal distribution when the noise level is 1*102. Fig. 29 is a curve chart showing the inverted PSD under 185/666 nm bimodal distribution when the noise level is 1*10, Fig. 30 is a curve chart showing the inverted PSD under 185/666 nm bimodal distribution when the noise level is 1*10°2, Fig. 31 is a curve chart showing the inverted PSD under 185/666 nm bimodal distribution when the noise level of 1*102, Fig. 32 is a curve chart showing the inverted PSD under 335/840 nm bimodal distribution when the noise level is 1*104. Fig. 33 is a curve chart showing the inverted PSD under 335/840 nm bimodal distribution when the noise level is 1*10°3, Fig. 34 is a curve chart showing the inverted PSD under 335/840 nm bimodal distribution when the noise level is 1*102, Detailed Description Figs. 1-34 show optimal embodiments of the present invention.
    The present invention will be further described below in combination with Figs. 1-34. As shown in Fig. 1, a dynamic light scattering inversion method of non-negative TSVD for adaptive sampling of particle size distribution, comprising the following steps: Step 1001. determining initial parameters; determining that the initial value of the number s of particle size distribution points is s=30 and the step length / is equal to 5, defining a counting constant as í, and letting the initial value of / be equal to 1.
    The conclusion that the initial value of the number s of particle size distribution points is set to s=30 is obtained after analyzing the influence of different number of sampling points on the 5 non-negative TSVD inversion result. The specific analysis process is as follows: First, simulating 374 nm unimodal wide distribution, 398 nm unimodal narrow distribution, 170/421 nm bimodal distribution, 185/666 nm bimodal distribution and 335/840 nm bimodal distribution. Simulation experiment conditions are as follows: incident light wavelength: 632.8 nm; Boltzmann constant: 1.3807*1023 J/K; scattering angle: 90°; measured temperature: 298.15 K; viscosity coefficient of water: 0.89*103 Pa.s; and refractive index of dispersion medium (water):
    1.331.
    Johnson's SB distribution is used when simulating unimodal distribution and simulating bimodal distribution. The expression thereof is: / Oel 11-4] cop os eon] | i.
    where u and o represent distribution parameters, different particle size distributions may be simulated by adjusting the parameters; Xmax and Xmin represent maximum particle diameter and minimum particle diameter respectively; and t=(X-Xmin)/(Xmax-Xmin) represents normalized size.
    As an important indicator to measure PSD inversion accuracy, relative error (hereinafter referred to as RE) represents the error between the inverted PSD and the theoretical PSD, the smaller the relative error is, the better the inversion result accuracy is. The expression thereof is: RE=|x-xt|2/]|x|2 (2) where x represents theoretical PSD, and x represents inverted PSD.
    When analyzing the influence of different humber of sampling points on the non-negative TSVD inversion result, the above unimodal distribution and bimodal distribution are simulated, and the relative errors (RE) of particle size distribution under different sampling points when the number of fixed channels is 120 and the noise level is 1*103 are calculated respectively, as shown in Figs. 2-6. It can be seen from the figures that when the number of sampling points is between 10 and 120, the relative error between the unimodal distribution and the bimodal distribution fluctuates between 0 and 1 with a small fluctuation range, and decreases with the increase of the number of sampling points in general. If the number of sampling points is greater than the number 120 of correlation function channels, the value of the relative error increases rapidly; if the number of sampling points is between 120 and 190, the value of the relative error increases slowly; and if the number of sampling points is greater than 190, the value of the relative error increases rapidly once again. With the substantial increase of the relative error, the accuracy of the inversion result drops sharply.
    Taking 398 nm unimodal narrow distribution and 170/421 nm bimodal distribution as examples, the inversion results when the number of sampling points is from 10 to 150 are simulated respectively when the number of channels is 120. The inversion results differ greatly under different number of sampling points. As shown in Figs. 7 and 10, when the number of sampling points is between 10 and 50, although PSD can be obtained from both unimodal distribution and bimodal distribution, the inversion results have poor smoothness and different levels of burrs, and the deviation between the peak position and the real PSD is large. When the number of bimodal distribution sampling points is too few, the inversion results have no obvious bimodal distribution feature, the overall error is large, and the error becomes more obvious as the number of sampling points decreases. Therefore, the number of sampling points should not be less, so the initial value of the number s of particle size distribution points is set to 30.
    As further shown in Figs. 8 and 11, the smoothness of the inversion results and the accuracy of the peak position are greatly improved with the increase of the number of sampling points, but the accuracy of the inversion results is not gradually improved with the increase of the number of sampling points. As clearly shown in Figs. 9 and 12, PSD cannot be inverted when the number of sampling points is greater than the number 120 of correlation function channels. Therefore, the influence of the number of sampling points on the accuracy of inverted PSD is proved through Figs. 7-12 simultaneously.
    Step 1002. Inverting particle size distribution of particles adopting the non-negative TSVD regularization principle; in the measurement process of dynamic light scattering (hereinafter referred to as DLS), for a polydisperse particle system, the normalized electric field autocorrelation function is: glv)= [ain exp{-Tr]}dr {3} where T represents delay time, [ represents attenuate linewidth, G (T) represents attenuate linewidth distribution function, and satisfies [Gre =1.
    The relationship between the attenuate linewidth and the particle diameter of particles is: T=Dg + D= + d lins (4) where D represents translational diffusion coefficient, q represents scattered wave vector, T represents absolute temperature, d represents particle diameter of particles to be measured, © represents scattering angle, A represents wavelength of laser in vacuum, rn represents viscosity coefficient of solution, n represents refractive index of solution, and ks represents Boltzmann constant.
    The formula (3) may be discretized into: gle )= Nar Jesp{-F 7, Ji=12. 8 =12.0) (5)
    where M represents the number of correlation channels of a correlator, and N represents the number of particles measured. By solving the formulas (3)-(5), the particle diameter of particles to be measured may be solved.
    The formula (5) may be simplified into: > Ax=g (6) where g=g(T;), x=G{[j), and A represents kernel matrix corresponding to the electric field autocorrelation function, the element thereof being exp(-[iT;}, the equation being a first kind of Freholm integral equation.
    The basic principle of non-negative truncated singular value decomposition (TSVD) regularization is to conduct singular value decomposition on a matrix A, remove the small singular value which has an amplification effect on the error, reduce the ill-condition of the equation (6), and then improve the accuracy of the solution, to obtain formula (7): AE EF = Tu a (3 where AeR™¢ u and v respectively represent left singular value vector and right singular value vector of the matrix A, and oi represent singular value. Through the formulae (6) and (7), it can be obtained: HO 7 | X= 2 (8) The formula (8) shows that the small singular value has an amplification effect on the error, so the small singular value should be truncated by selecting a regularization parameter in order to avoid the influence of the small singular value. Thus, the formula (7) is transformed into: x A4 =S won i (9} where k represents regularization parameter, and Ax represents kernel matrix corresponding to the electric field autocorrelation function after the small singular value is truncated. Thus, the expression of non-negative TSVD is: f(x)=minA4, x- gl SEX 20 (103 For the selection of the regularization parameter, the L-curve method widely used in the art is adopted herein.
    Step 1003. Reconstructing electric field autocorrelation functions, and calculating residuals of the electric field autocorrelation functions with the actually measured electric field ACF; because the theoretical distribution of the particle diameter of particles to be measured is not known in the actual measurement process, the optimal sampling point number cannot be selected according to the minimum relative error of particle size distribution. In order to select optimal particle size distribution sampling points, the inversion accuracy is improved. Therefore, in the present application, taking 398 nm unimodal narrow distribution and 170/421 nm bimodal distribution when the number of channels is 120 as examples, according to the above analysis, the number of particle size distribution sampling points is less than the number of channels and the minimum number of particle size distribution sampling points is 30 in general, when the noise level is 1*103, the relative error (RE) of particle size distribution and the residual (RES) of the electric field autocorrelation function when the number of particle size distribution sampling points is 30-120 are simulated, as shown in Figs. 13-16.
    As clearly shown in Figs. 13-16, there is a certain relationship between the relative error and the residual. The relative errors of particle size distribution of the unimodal distribution and the bimodal distribution are weakly similar to the residuals of the electric field autocorrelation functions corresponding thereto, with the change in the number of sampling points, the fluctuation trends of the two are roughly identical, and both can reach the minimum under the same number of sampling points. Thus, the expression of the residuals (RESs) of the electric field autocorrelation functions under the number s of current sampling points is obtained: RESs=|9(Ts)-g:(T)|[2 (11) where s represents the number of sampling points, as shown in the above formula (6), g(Ts)=AsPSD:s represents the reconstructed electric field ACF, and g:(T) represents the actually measured electric field ACF.
    Step 1004. Assigning the residuals RES: of the electric field autocorrelation functions calculated in the step 1003 to RES;; Step 1005. Increasing the number of particle size distribution sampling points, wherein the increase in the number of particle size distribution sampling points is the value of one step length; Step 1006. Determining whether the number of current particle size distribution sampling points is greater than the number of correlation function channels; determining whether the number of current particle size distribution sampling points is greater than the number of autocorrelation function channels, if the number of current particle size distribution sampling points is less than or equal to the number of autocorrelation function channels, returning to step 1002 and loop-executing steps 1002-1005, and if the number of current particle size distribution sampling points is greater than the number of autocorrelation function channels, jumping out of the loop and executing step 1007; the reason why the number s of particle size distribution sampling points should be less than or equal to the number m of autocorrelation function channels (that is, the maximum number s of sampling points selected should be the number m of the autocorrelation function channels) is that: in order to verify that the selection of the maximum number of optimal sampling points is affected by the number of channels, 80, 160 and 210 channels are respectively selected in number, taking 398 nm unimodal narrow distribution as an example, the relative error and inverted PSD of particle size distribution under different sampling points are simulated when the noise level is 1*1073.
    Figs. 17-19 are curve charts respectively showing the relative error under different number of sampling points of 398 nm unimodal narrow distribution when the number of channels is 80, 160 and 210. Figs. 20-21 are curve charts showing the inverted PSD under different number of sampling points of 398 nm unimodal narrow distribution when the number of channels is 80. Figs.
    22-23 are curve charts showing the inverted PSD under different number of sampling points of 398 nm unimodal narrow distribution when the number of channels is 160. Figs. 24-25 are curve charts showing the inverted PSD under different number of sampling points of 398 nm unimodal narrow distribution when the number of channels is 210. As shown in the figures, for different number of channels, if the number of sampling points is less than the number of channels, PSD may be obtained; if the number of sampling points is too few, the inversion accuracy may decrease correspondingly; and if the number of sampling points is greater than the number of channels, the relative error may increase rapidly and the inverted PSD may deviate from the real PSD seriously. Thus, the number of channels limits the selection of the maximum number of sampling points.
    The reason for this phenomenon is that: when solving the ill-conditioned problem Ax=g adopting non-negative TSVD, there is a need to conduct singular value decomposition on the matrix AeR™s, where m represents the number of channels, and s represents the number of sampling points. If mzs, a singular value of the matrix A is decomposed into: A=UIV = > ov] (12) bad where U=(u:, Uz, … Us)ER™S, V=(v4, va, … , Vs)ERS™, J=diag(0:,02, .., Os)ERS™, the number of singular values is s, the rank r(A) of the matrix A is equal to s, and the rank #14} of the augmented matrix A=[Aig|of the equation set Ax=g is equal to s, so slob {A =3 the solution of the equation set Ax=g is unique, and the non-negative TSVD may fit approximate results (as shown in Figs. 7-8, Figs. 10-11, Fig. 20, Fig. 22 and Fig. 24).
    However, when m is far greater than s, the amount of data measured in the experiment is far greater than the amount of data required for small sampling points, so the information utilization rate is low, resulting in low inversion result accuracy and poor smoothness (as shown in fixed-20 curves in Fig. 7, Fig. 10 and Fig. 20, the fixed-40 curve in Fig. 22 and fixed-50 curve in Fig. 24).
    If m<s, the singular value of the matrix A is decomposed into: A=UEV =S uc’ (13) isd where U=(us, Uz, … Um)ERTT, V={vs, V2, … , Vm)ER®™ > =diag(0:,02, … , 0s)ER™™, the number of singular values is m, the rank r(A) of the matrix A is equal to m7, and the rank ra) of the augmented matrix 4 =[.4:¢] of the equation set Ax=g is equal to m, so {dbo rd dj the solution of the equation set Ax=g is not unique, and non-negative TSVD cannot fit approximate results from infinite solutions (as shown in Fig. 9, Fig. 12, Fig. 21, Fig. 23 and Fig. 25). Thus, the condition to select sampling points is ssm, namely, the maximum number s of sampling points selected is the number m of autocorrelation function channels.
    Step 1007. Calculating the minimum value of the residuals of the electric field autocorrelation functions;
    3 selecting a minimum value from a plurality of RES; values saved in the step 1004 as the minimum value of the residuals of the electric field autocorrelation functions, and on the basis of the above formula 11, proposing a criterion for determining optimal sampling point number according to the minimum value of the residuals (RESs) of the electric field autocorrelation functions, namely:
    10 RESma=min(|9(Ts)-9:(T)|[2) (14) where s represents the number of sampling points, (1s)=AsDSPs represents the reconstructed electric field autocorrelation function, and g:(T) represents the actually measured electric field autocorrelation function.
    Step 1008. Obtaining the optimal sampling point number corresponding to the minimum value of the residuals of the electric field autocorrelation functions; after obtaining the minimum value of the residuals of the electric field autocorrelation functions in the step 1007, the number s of sampling points corresponding to the value is the optimal sampling point number.
    Step 1009. Obtaining the particle size distribution of the particles corresponding to the optimal sampling point number.
    Verification of the dynamic light scattering inversion method of non-negative TSVD for adaptive sampling of particle size distribution: In order to verify the validity of the dynamic light scattering inversion method of non-negative TSVD for adaptive sampling of particle size distribution, autocorrelation functions under different particles (bimodal distribution) and different noise levels (1*10-4, 1*103, 1*10 ) are inverted using the fixed sampling point number non-negative TSVD algorithm and the dynamic light scattering inversion method of non-negative TSVD for adaptive sampling of particle size distribution respectively, and the inversion results are compared.
    The autocorrelation function with noise is obtained by adding Gaussian noise, and the expression thereof is as follows: Goele) = (5, ) + 00{r) (15) where Ge 75) represents electric field autocorrelation function data with noise, g(t) represents electric field autocorrelation function data without noise, ò represents noise level, and n(T) represents Gaussian noise.
    In order to better describe the inversion results of the two methods, two performance indexes are introduced: (1) Relative error (RE, as shown in formula 2).
    (2) Error of peak position (EPP): representing the error between the inverted peak position and the real peak position: PVE=|pv-pv/pvt (16) where Xx, xi, pv and pv; respectively represent inverted PSD, theoretical PSD, inverted peak position and real peak position.
    Figs 26-28 show the inversion results of 170/421 nm bimodal distribution, the sampling points selected by adopting the adaptive sampling point number algorithm are respectively 70, 115, 110 in number when the noise levels are 1*10%, 1*10:3 and 1*102. As shown in the figures, under different noise levels, when the fixed sampling points are 50 in number, the error of peak position and relative error of the inverted PSD are both large, and the smoothness is poor. When the fixed sampling points are 80 and 100 in number, the accuracy of the inverted PSD is improved to a certain extent, but it is significantly lower than that obtained by adopting the adaptive algorithm. The inverted PSD obtained by adopting the adaptive algorithm is more consistent with the theoretical PSD.
    Figs. 29-31 show the inversion results of 185/666 nm bimodal distribution and corresponding performance indexes, the sampling points selected by adopting the adaptive sampling point number algorithm are respectively 60, 95, 120 in number when the noise levels are 1*104, 1*10° 3and 1*102. As shown in the figures, under the noise level of 1*102, when the fixed sampling points are 50 in number, the inverted PSD has no bimodal feature and has large error. Under three noise levels, when the fixed sampling points are 50, 80 and 100 in number, the inverted PSD all have burrs of different size, so relatively speaking, the adaptive algorithm has better smoothness. The error of peak position and relative error of PSD obtained by adopting the adaptive algorithm are obviously lower than those obtained by adopting the fixed algorithm.
    Figs 32-32 show that for 335/840 nm bimodal distribution, the sampling points selected by adopting the adaptive sampling point number algorithm are respectively 70, 60, 75 in number when the noise levels are 1*10%, 1*10:3 and 1*102. Under three noise levels, when the fixed sampling points are 50 in number, the inverted PSD has no bimodal feature. Under the noise level of 1¥102, when the fixed sampling points are 80 and 100 in number, the inverted PSD have no bimodal distribution feature. While the inverted PSD obtained by adopting the adaptive algorithm have obvious bimodal distribution features under different noise levels, the inverted PSD is closer to the theoretical PSD, and the anti-noise performance is higher.
    To sum up, for bimodal distribution, under different noise levels, the relative error and error of peak position of the inverted PSD obtained by adopting the dynamic light scattering inversion method of non-negative TSVD for adaptive sampling of particle size distribution are less than those obtained by adopting the fixed algorithm. With the size increase of mixed particles in the bimodal distribution, the deviation between the inverted PSD of the fixed algorithm and the theoretical PSD gradually increases, and the inverted PSD has no bimodal distribution feature at a high noise level; while the inverted PSD of the adaptive algorithm is significantly improved, and has obvious bimodal distribution features at different noise levels. For 335/840 nm bimodal distribution, under three noise levels, all the inverted PSD obtained by adopting the adaptive algorithm have obvious bimodal distribution features. Therefore, the dynamic light scattering inversion method of non-negative TSVD for adaptive sampling of particle size distribution improves the accuracy of inversion results, has a wide range of application and high anti-noise capability.
    The above only describes preferred embodiments of the present invention, not intended to limit the present invention in other forms. Any of those skilled in the art familiar with field may change or vary the embodiments through the technical contents disclosed above into equivalent embodiments with equivalent modification. However, any simple amendment, equivalent change and variation made to the above embodiments according to the technical essence of the present invention without departing from contents of technical solutions of the present invention shall still belong to the protection scope of the technical solutions of the present invention.
    权利要求:
    Claims (5)
    [1]
    A method of dynamic light scattering inversion of non-negative TSVD for adaptive sampling for a particle size distribution, the method comprising the steps of: step 1001: determination of the initial parameters; step 1002: inverting the particle size distribution using the non-negative TSVD regularization principle; step 1003: reconstructing electric field autocorrelation functions, and calculating the residuals of the electric field autocorrelation functions with the actually measured electric field ACF; step 1004: storing the residuals of the electric field autocorrelation functions calculated in step 1003; step 1005: increasing the number of particle size distribution points; step 1006: determine whether the number of current sample points for the particle size distribution meets a trigger condition, and if so, perform step 1007, otherwise return to steps 1002 - 1005; step 1007: calculating the minimum value of the residuals of the electric field autocorrelation functions; step 1008: obtaining the optimum number of sampling points corresponding to the minimum value of the residuals of the electric field autocorrect functions; and step 1009: obtaining the particle size distribution of the particles corresponding to the optimum number of sampling points.
    [2]
    The method of dynamic light scattering inversion of non-negative TSVD for adaptive sampling for a particle size distribution according to claim 1, wherein the trigger condition in step 1008 is that the number of particle size distribution sampling points is greater than the number of correlation function channels.
    [3]
    The method of dynamic light scattering inversion of non-negative TSVD for adaptive sampling for a particle size distribution according to claim 1, wherein the initial parameters in the step 1001 are: the initial value of the number s of the particle size distribution point: s = 30, the step length ! : equal to 5.
    [4]
    The method of dynamic light scattering inversion of non-negative TSVD for adaptive sampling for a particle size distribution according to claim 1, wherein the expression of the minimum value of the residuals of the electric field autocorrelation functions in the step 1007 is: RESmia = min(| g(ts)-g1(1)1|2), where s represents the number of sampling points, g(ts) = AsPSDs represents the reconstructed electric field autocorrelation function, and g+(1) represents the actually measured electrical field autocorrelation function.
    [5]
    The method of dynamic light scattering inversion of non-negative TSVD for adaptive sampling for a particle size distribution according to claim 2, wherein in the step 1005, the increment of the number of sampling points for the particle size distribution is the value of a step length.
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    公开号 | 公开日
    NL2026543B1|2021-11-09|
    CN110595962A|2019-12-20|
    CN110595962B|2021-11-30|
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    CN201910930174.0A|CN110595962B|2019-09-29|2019-09-29|Non-negative TSVD dynamic light scattering inversion method for self-adaptive sampling of particle size distribution|
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