Research On Retrieval Algorithm Of Particle Size Distribution Based On Spectral Extinction Method

With the rapid development of scientific field and the appearance of all kindsof new materials, there are more and more technical problems correlated withparticle issues, and the measurement of particle size distribution (PSD) has becomeone of the most important research fields. Among all the particle size measuringmethods, spectral extinction method is probably the most attractive one due to itstheoretical simplicity and convenience and its realization of measurement on micronor sub-micron particle systems. In particular, with the urgent demand for in situmeasurements of PSD, the spectral extinction method has shown greatdevelopments and potential applications.In spectral extinction particle sizing method, the PSD can be retrieved by someinversion methods using the extinction values of multiple wavelengths. Owing toserious oscillation of the extinction efficiency, the data processing of this method isrelated to the solution of a Fredholm integral equation of the first kind. It is a wellknown typical ill-posed problem, and there are significant difficulties for solvingthe theoretical solution of this problem. Therefore, the development of rapid andefficient retrieval algorithms for recovering the PSD has received increasedattention and concerns by many researchers. This subject is supported by theNational Natural Science Foundation of China (No.61071036). The objective of thissubject is to investigate accurate and fast retrieval algorithms of PSD based on thespectral extinction method, which can solve the problems along with highcomplexity of whole retrieval process, low retrieval speed, and instability of theretrieval results, thus making the spectral extinction method more suitable foronline particle sizing.This study is firstly focused on the selection of optimal wavelengths inmultispectral region. In the PSD retrieval process, the extinction values of eachincident wavelength may involve different amount of information about the PSD.The traditional measurement is performed only within a narrow spectral region (i.e.visible spectrum region), which may result in the decrease of accuracy andanti-noise effect of the retrieval results to some degree. Furthermore, consideringboth rapidity and simplicity in many practical industrial occasions, only limitedprincipal wavelengths can be chosen to deal in the data processing. Therefore,according to the degree of correlation for extinction efficiency of differentwavelengths, the method of sectional optimal wavelength selection in multispectralregion is presented. In the ultraviolet-visible-near-infrared spectrum region, theprincipal wavelengths selected in each spectrum region, which own high correlation of extinction efficiency with all other wavelengths and share low correlation ofextinction efficiency each other, constitute the whole optimum wavelengths ofmultispectral range to retrieve the PSD. For the case that the number of wavelengthsis less than particle subintervals which can result in the deficiency of information,the less optimum wavelengths involve most amount of information about the PSD,therefore the measuring accuracy can be effectively ensured and the computationtime of the whole retrieval can be significantly reduced. The method of sectionaloptimal wavelength selection in multispectral region offers the theorical basis forthe retrieval of PSD in succeeding chapters.In spectral extinction particle sizing method, the calculation of extinctionefficiency is a critical issue which affects the accuracy and rapidity of the wholeretrieval. Aiming at overcoming complexity in theory, intricacy in calculation, lowconvergence speed, and instability for calculating the extinction efficiency ofspherical and spheroidal particles with rigorous methods, the approximate methodfor fast and accuracy retrieval is explored. The combination of Mie theory andgeneralized eikonal approximation (GEA) method is proposed in this paper tocalculate the extinction efficiency. Based on the extinction efficiency calculated bythe combined approximate method, the retrieval of PSD of spherical particles andspheroidal particles are then investigated. The combined approximate method, usedas an alternative to the rigorous Mie theory, not only can extend the applicablerange and guarantee the accuracy of the retrieval results, but also can simplify thecalculation process and improve the speed of the whole retrieval process. Theapproximate method can be used as an effective replacement when the rigoroussolutions suffer computational difficulties and numerical instability.The design or selection of inversion methods is one of the most importantaspects of the whole retrieval which can guarantee to obtain accurate and fastretrieval results. Considering the inversion methods for the retrieval of PSD are stillin stage of development, this paper focuses on the study of inversion method. Thepattern search algorithm combined with the Tikhonov smoothing functional for thedetermination of PSD is proposed. To ensure good rapidity and accuracy of thewhole search process, a competitive strategy about the pattern search algorithm isalso designed. In the inversion process, the PSD retrieval problem is firstformulated as a minimization problem, with the Tikhonov smoothing functionalemployed in modeling the objective function, and then the improved pattern searchalgorithm is applied to adjust the objective function until a given stopping criterionhas been achieved. The pattern search algorithm does not require any gradientinformation like many traditional methods; also it does not require complexselection and mutation of populations like many intelligent optimization algorithms;therefore making the inversion process more convenient and efficient. Experimental results indicate that the proposed algorithm can be successfully applied to retrievethe PSD with high reliability and stability. In condition of fully considering retrievalprecision and retrieval time, the proposed inversion method has certain advantage,which is more suitable for accurate and quick field measurement of particle sizing.Based on the theoretical analyses and numerical simulations, by using thestandard polystyrene samples offered by Beijing Institute of Nuclear Engineering,the three proposed methods, namely, the method of sectional optimal wavelengthselection in multispectral region, the retrieval algorithm of PSD based on the GEAmethod, the inversion method of improved pattern search algorithm for retrieval ofPSD, are further verified by the practical experimental data, and the retrieval resultsof PSD for standard polystyrene samples are also analyzed and studied. Theexperiments validate the feasibility and accuracy of the above proposed methods inpractical retrieval of PSD.