Particle Size Distribution Values Research Articles

Implementation of near-infrared spectroscopy and convolutional neural networks for predicting particle size distribution in fluidized bed granulation

Monitoring the particle size distribution (PSD) is crucial for controlling product quality during fluidized bed granulation. This paper proposed a rapid analytical method that quantifies the D10, D50, and D90 values using a Convolutional Block Attention Module-Convolutional Neural Network (CBAM-CNN) framework tailored for deep learning with near-infrared (NIR) spectroscopy. This innovative framework, which fuses CBAM with CNN, excels at extracting intricate features while prioritizing crucial ones, thereby facilitating the creation of a robust multi-output regression model. To expand the training dataset, we incorporated the C-Mixup algorithm, ensuring that the deep learning model was trained comprehensively. Additionally, the Bayesian optimization algorithm was introduced to optimize the hyperparameters, improving the prediction performance of the deep learning model. Compared with the commonly used Partial Least Squares (PLS), Support Vector Machine (SVM), and Artificial Neural Network (ANN) models, the CBAM-CNN model yielded higher prediction accuracy. Furthermore, the CBAM-CNN model avoided spectral preprocessing, preserved the spectral information to the maximum extent, and returned multiple predicted values at one time without degrading the prediction accuracy. Therefore, the CBAM-CNN model showed better prediction performance and modeling convenience for analyzing PSD values in fluidized bed granulation.

A new algorithmic approach for predicting the particle size distribution of dispersed soil suspensions using an automated optical settling column

Analyzing a large number of samples for their dispersive properties and particle size distribution (PSD) is often cumbersome and time-consuming, particularly when using traditional hydrometer or pipette-based methods. In this study, we analyzed the efficacy and rapidity of an automated, optical settling column (OSC) to measure the PSD of soils. The OSC provided backscattering and transmission intensity profiles at preprogrammed time intervals that illustrated sedimentation/flocculation processes of suspended particles, making the approach desirable for soil dispersion studies. Settling experiments were performed using 177 soil samples collected from 59 sampling locations across the United States. All soil samples were pretreated with sodium hexametaphosphate (HMP) to achieve maximum dispersion and analyzed with the OSC. The effects of settling run time and sampling frequency were also investigated. The results were compared with separate soil PSD data obtained using the common particle sizing analysis, the pipette method. Using feature engineering and dimensionality reduction, we created different novel methods of modeling the PSD data. Resampling was employed to compare accuracy of these novel methods by generating 300 instances of model performance for each method. We further estimated model generalization using two techniques: (i) a holdout (HO) estimation approach to suggest the “best-case” performance and (ii) an averaged model performance to provide a more conservative performance estimate. The best method studied here provided PSD values that deviated from those gathered through the pipette method by between 2.8% − 3.3% for clay, 5.7% − 9.4% for silt, and 6.5% − 9.6% for sand.

A new nanosuspension prepared with wet milling method for oral delivery of highly variable drug Cyclosporine A: development, optimization and in vivo evaluation

Cyclosporine A (CsA) is a cyclic polypeptide, that has been widely used for immunosuppression. This study aims to develop nanosuspension for oral administration of CsA using the wet milling (WM) method one of the top-down technologies. The WM method was optimized by studying the effects of critical process parameters for WM on the particle size (PS), particle size distribution (PDI), and zeta potential (ZP) of nanosuspensions using the Design of Experiment (DoE) approach. Nanosuspension was developed using hydroxypropyl methylcellulose (HPMC) and sodium dodecyl sulfate (SDS) and in vitro characterization studies were performed. In vitro dissolution and in vivo pharmacokinetic studies were conducted with biorelevant media (fasted and fed state simulated fluids) and fasted and fed states in rats, respectively. In vivo immunological studies were also performed. PS, PDI, and ZP values for nanosuspension were approximately 600 nm, 0.4, -25 mV, respectively. The solubility of CsA was increased by 4.5-folds by nanosuspensions. Dissolution studies showed that nanosuspension had higher dissolution than the commercial product in the FeSSIF medium. The pharmacokinetic study indicated that AUC0–24 values of CsA nanosuspension were to be 2.09 and 5.51-fold higher than coarse powder in fasted and fed conditions, respectively. Immunological studies were carried out after oral administration of nanosuspension for 21 days, the ratio of CD4+/CD8+ was found to be more acceptable than the commercial product. These results demonstrated that nanosuspension is a promising approach for increasing the bioavailability and avoiding the food effect on absorption of CsA which one of the highly variable drugs.

Development of a high temperature resistant nano-plugging agent and the plugging performance of multi-scale micropores

Nano-plugging agents (NPAs) are very important to stabilize the wellbore by reducing pressure transmission and drilling fluid invasion during drilling engineering. A functionalized polystyrene latex (FPL) was synthesized by micellar polymerization as a NPA for drilling fluids. The particle size and thermal stability of FPL were characterized by particle size analysis and thermogravimetric analysis (TGA). The experimental results showed that the initial thermal decomposition temperature of FPL was 310.6 ℃. The medium value of particle size distribution (D50) of FPL decreased from to 371–235 nm after aging at 220 ℃, indicating that FPL had good temperature resistance property. The plugging method and plugging performance of FPL for four filter media with pore sizes from 0.01 µm to 10 µm were introduced. FPL itself was difficult to plug the filter papers and ceramic filter disks, but FPL could reduce fluid loss of bentonite suspensions. SEM observation indicates that FPL could improve the quality of mud cakes and plug the small pores of ceramic filter disks. For microporous membranes and artificial mud cakes with low permeability, FPL aqueous suspensions had a good plugging performance. The plugging experimental results conformed well to the 2/3 bridging rule. This paper provides a good reference for the development of high temperature NPAs and the establishment of evaluation methods of NPAs.

Determination of the Effect of Soil Particle Size Distribution on the Shear Behavior of Sand

Many geotechnical problems require the determination of soil engineering properties such as shear strength. Therefore, the determination of the reliable values for this parameter is essential. For this purpose, the direct shear test, as one of the oldest tests to examine the shear strength of soils, is the most common way in laboratories to determine the shear parameters of soil. There are far too many variables that influence the results of a direct shear test. In this paper, a series of 10 × 10 cm direct shear tests were carried out on four different poorly graded sands with different particle size distributions to determine their shear behaviors. Four different poorly graded sands with a different median diameter or medium value of particle size distribution (D50) (0.2, 0.53, 1.3, and 2.3 mm) has been selected, and about 40 direct shear tests were conducted. It was concluded that a soil’s friction angle is affected by coarse-grained material. Accordingly, sandy soils with bigger particle sizes record a higher friction angle than soils containing small particles. The investigations also showed that sand with bigger particle sizes has a higher dilation angle. In addition, a non-linear regression analysis was performed to establish the exact relationship between the friction angle of the soil and the characteristics of the soil particles. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

Characterization and physicochemical properties analysis of konjac glucomannan: Implications for structure-properties relationships

The objective of this research was to identify the structural and physicochemical factors of konjac glucomannan (KGM). Seven purified konjac flours that varied in hydration behavior and ultimate viscosity were selected and their compositional, molecular structural, and morphological properties were compared. The results suggested that the hydration rate and the development of solution viscosity were related to particle size and surface morphology of KGM particles rather than molecular structure. The particle size distribution value, D95, varied from 452.70 μm to 132.30 μm and the hydration time decreased from 90 min to 8 min, respectively. The ultimate viscosity of fully hydrated KGM solutions was not always associated with higher Mw. Our results show that lower main chain mannose to glucose (M/G) ratios led to lower viscosity and higher acetyl content exhibited higher viscosity compared to low-acetyl KGM of same Mw. The ultimate viscosity was found to be related to a greater degree of intermolecular interaction at concentrations above c*, indicated by higher n2 values, which is the slope of double logarithmic plots of ‘zero-shear’ specific viscosity versus degree of space occupancy (c[η]). Small angle x-ray scattering (SAXS) results suggested that molecular conformation was the key factor that affected n2, the larger hydrodynamic volume and greater intermolecular interactions that contributed to the larger n2. The results of this research identify physicochemical factors that are necessary for rational KGM structural design as a satiating ingredient in appetite regulation and body weight management.

Synthesis of folic acid functionalized terbium-doped dendritic fibrous nano-silica and Interaction with HEK 293 normal, MDA breast cancer and HT 29 colon cancer cells.

A novel folic acid functionalized terbium-doped dendritic fibrous nanoparticle (Tb@KCC-1-NH2 -FA) with high surface area was synthesized using a novel hydrothermal protocol. In the present work, we report the fluorescent Tb-doted nanomaterial with emission wavelength at 497 nm which confirms the formation of Tb@KCC-1-NH2 -FA. Synthesized nanoparticles were investigated through transmission electron microscope, field emission scanning electron Microscopy, Fourier transform infrared spectra, Brunauer-Emmett-Teller, energy dispersive X-ray, Zeta potential and particle size distribution values and AFM (Atomic force microscopy) techniques. Specially, our desired nanomaterial which has FA moieties on the surface of Tb@KCC-1-NH2-FA where interact with folate receptor (FR) which there is on the surface of the various cancer cells. For this purpose, fluorescence microscopy images were used to prove the uptake of FA based nanomaterial with FR-positive MDA breast cancer and HT 29 colon cancer cells. Also HEK 293 normal cells as FR-negative cells verified the specificity of our desired nanomaterial toward the FR-positive cells. The cytotoxicity survey of Tb@KCC-1-NH2 -FA was examined by MTT assays against MDA breast cancer, HT 29 colon cancer and HEK 293 Normal cell lines which confirmed their biocompatible nature with any significant cytotoxic effects even for concentration higher than 900 μg/mL which could be used as a non-toxic catalyst or carrier in biological ambient. Hence, Tb@KCC-1-NH2 -FA were synthesized using green and hydrothermal method; the process was simple with good productivity and desired nanocomposite was non-toxic.

Optimization and in vitro evaluation of ziprasidone nanosuspensions produced by a top-down approach

The main purpose of this study was to develop nanosuspensions of ziprasidone hydrochloride monohydrate (ZHM), the BCS Class II antipsychotic agent, to solve its water solubility issues, improve oral bioavailability, and reduce the food effect. Microfluidization method was used to obtain nanosuspensions. Effects of formulation and process parameters on particle size (PS), particle size distribution (PDI), and zeta potential (ZP) values were investigated by Design of Experiment (DoE) approach. The Solubility of ZHM in water was determined. The dissolution studies were performed in various media and also FaSSIF and FeSSIF media in comparison with coarse powder, physical mixture, and commercial product. The nanosuspensions were also characterized by SEM, XRPD, DSC. The optimum PS, PDI and ZP values were found with the nanosuspensions stabilized with PVP and Vitamin E. Round shape particles were observed and thermal properties of ZHM were preserved. The solubility was increased 2.3-fold and 1.84-fold with PVP K30 and Vitamin E TPGS stabilized nanosuspensions compared with ZHM coarse powder, respectively. Nanosuspensions showed >95% dissolution in FeSSIF medium and 80% in FaSSIF medium. In conclusion, ZHM nanosuspensions which was prepared by microfluidization using DoE can enhance water solubility and dissolution as well as decrease the fed/fasted state variations.

Morphology and Kinetics Evolution of Nanoscale Phase in Fe⁻Cr Alloys under External Strain.

Uniaxial strain was applied to aging Fe–Cr alloys to study the morphological orientation and kinetics of the nanoscale α′ phase by utilizing phase-field simulation. The effects of applied uniaxial compressive and tensile strain on the two and three-dimensional morphology as well as on the separation kinetics of the α′ phase are quantitatively clarified. Compared with the applied uniaxial tensile strain, the applied uniaxial compressive strain shows a greater effect on the rate of phase separation, lath shape morphology and an increased rate of growth and coarsening in the α′ phase, the boundary of the α + α′ phase region is widened influenced by the applied compressive strain, while the applied tensile strain results in an increase of particle number density and a decrease of particle radius. The peak value of particle size distribution of the α′ phase increases with aging time, while an opposite trend is shown under the applied strain, and there is an obvious deviation from the theoretical distribution of Lifshitz–Slyozov–Wagner under compressive strain. The orientation morphology and kinetic change show the substantial effects of applied strain on the phase separation and supplies the method for the morphological control of nanoscale particles.

Effect of organic alkali on compressive strength and hydration of wet-grinded granulated blast-furnace slag containing Portland cement

In this study, a commercially available ground granulated blast-furnace slag (GGBS) was further processed by wet grinding, and WGGBS (wet-grinded GGBS) slurry with superfine particles was obtained. To avoid self-hydration of slag and augment the grinding efficiency, one commercially available polycarboxylate superplasticizer was added. The binder, composed of 10.0% cement and 90.0% WGGBS with the addition of 0.05% triethanolamine (TEA) and 0.05% triisopropanolamine (TIPA), was designed; the cement was added to provide alkali environment and calcium ions, and organic alkali was used to promote the dissolution of GGBS. The compressive strength of mortar and hydration mechanism was investigated. The results showed that wet grinding exhibited high grinding efficiency; D(50) value of particle size distribution of WGGBS was reduced from 18 μm to 2.10 μm by wet grinding for one hour. Compressive strength of hardened WGGBS mortar was 20 MPa and 28 MPa at 7 d and 28 d, and 10% cement replacement ratio of the WGGBS increased the strength to 24.6 MP at 7 d and 32.2 MPa at 28 d. Furthermore, in C-WGGBS, 0.05% TEA increased the 7 d strength by 23%, with the value of 30.27 MPa, but 0.05%TIPA slightly reduced it to 23.5 MPa, with a decrease by 5%. Mechanism behind the increase was due to the accelerated formation of hydrotalcite-like phase, despite the retarding effect on formation of C-(A)S-H gel; the slight decline by TIPA was mainly because of the retarding effect of formation of C-(A)S-H gel as well as its air-entraining effect. Moreover, both TEA and TIPA increased the 28 d strength of cement-WGGBS system, because TEA and TIPA were able to facilitate ferric and aluminum dissolution and expedite the formation of C-(A)S-H gel as well as hydrotalcite-like phase. Additionally, it was worth noting that 0.05% TEA could make 28 d strength of the binder, composed of only 10% cement, reach 43.7 MPa, in accordance with the requirement of 42.5 grade cement.

Effects of the variation in diesel fuel components on the particulate matter and unregulated gaseous emissions from a common rail diesel engine

Diesel fuel mainly contains n-alkanes, iso-alkanes, cycloalkanes and aromatics, and varies with the source of crude oil and refining process. Although satisfying the same emission regulation, the particulate matter (PM) emissions and unregulated gaseous emissions of diesel fuel maybe vary a lot due to different fuel components. A series of experiments was conducted on a single-cylinder diesel engine fueled with diesel respectively blending with 10% and 20% fuel components to study the aldehyde, olefins, methane emissions and particulate matter (PM) emissions under engine loads from indicated mean effective pressure (IMEP) 1 bar to 8 bar. In this study, n-dodecane, iso-dodecane, tetralin and decalin were chosen to represent n-alkanes, iso-alkanes, aromatics and cycloalkanes, respectively. The results show that when IMEP less than 4 bar, the aldehydes emissions are relatively high even above 100 ppm. Blending fuel components in diesel causes the aldehydes emissions increasing except for n-alkanes. At low load from IMEP 1 to 3 bar, as blending ratio increase, aromatics and iso-alkanes noticeably worsen the hydrocarbon emissions especially. The hydrocarbon emissions of diesel/20% iso-dodecane and diesel/20% tetralin are respectively more than twice over those of diesel/10% iso-dodecane and diesel/10% tetralin. Aromatics and cycloalkanes have relatively high-level particle numbers which mainly distribute in nucleation mode with diameter ranging from 10 nm to 50 nm at IMEP 1 bar and 2 bar because of their lower H/C ratio leading to a tendency for precursor formation. At heavy load, the particle number presents a regular pattern that n-alkanes > cycloalkanes > iso-alkanes > aromatics and the peak value of particle size distribution moving towards to the right side due to prolonged combustion duration resulting in more time to polymerize.

Precipitation kinetics of γ phase in an inverse Ni–Al alloy

The precipitation kinetics of γ phase in the inverse Ni–20.4 at. % Al alloy are studied by utilizing phase-field method, combining with the volume fraction, particles number density, average particle radius, average aspect ratio and particle size distribution (PSD) of γ phase at different aging temperatures. It is found that the decrease rate of particles number density increases with the elevated aging temperature, and the decrease rate in the early coarsening stage are greater than that in the stable coarsening stage. The average particle radius shows a linear relationship with time through kt1/3 in the stable coarsening stage of the inverse Ni–Al alloy, and the coarsening rate constant k increases with the elevated temperature. As the aging progresses, the peak value of PSD becomes smaller and the normalized radius r/<r> moves from 1.1 to 1.0, while the peak value of PSD becomes larger and the corresponding r/<r> value moves from 0.9 to 1.0 with the elevated temperature. The peak value of PSD is less than that predicted by Lifshitz-Slyozov-Wagner (LSW) theory at different aging temperatures.

Dynamics evolution of γ′ precipitates size and composition interface between γ/γ′ phases in Ni–Al alloy at different aging temperatures

The precipitation dynamics of γ′ (L12-Ni3Al) phase and composition interfacial width between γ (fcc Ni) and γ′ phase were investigated using the phase field simulation linking with CALPHAD method. The coarsening rate and particle size distribution (PSD) of γ′ phase, the temporal composition interfacial width of γ/γ′ in Ni–17 at% Al alloy aged at 923, 973 and 1023 K were clarified. As the aging temperature increases, the morphology of γ′ phase changes from the interconnected rectangle shape to the separated cuboidal shape. The average particle radius ( ) of γ′ phase at coarsening stage follows ∝ t n with the exponents n = 0.21, 0.23 and 0.26, respectively. The peak values of simulated PSDs at 923 K are less than the value calculated by the Lifshitz–Slyozov–Wagner (LSW) model, and the width of simulated PSD increases at later stage of precipitation. The normalized radius (r/ ) which corresponds to the peak value of PSD moves from 1.1 to 1.0 as the aging temperature increases from 923 to 1023 K, and they are smaller than that of LSW model. The composition interfacial width decreases as the aging progresses and increases as the aging temperature increases.

The Effect of Particle Size Distribution on the Design of Urban Stormwater Control Measures

An urban pollutant loading model was used to demonstrate how incorrect assumptions on the particle size distribution (PSD) in urban runoff can alter the design characteristics of stormwater control measures (SCMs) used to remove solids in stormwater. Field-measured PSD, although highly variable, is generally coarser than the widely-accepted PSD characterized by the Nationwide Urban Runoff Program (NURP). PSDs can be predicted based on environmental surrogate data. There were no appreciable differences in predicted PSD when grouped by season. Model simulations of a wet detention pond and catch basin showed a much smaller surface area is needed to achieve the same level of solids removal using the median value of field-measured PSD as compared to NURP PSD. Therefore, SCMs that used the NURP PSD in the design process could be unnecessarily oversized. The median of measured PSDs, although more site-specific than NURP PSDs, could still misrepresent the efficiency of an SCM because it may not adequately capture the variability of individual runoff events. Future pollutant loading models may account for this variability through regression with environmental surrogates, but until then, without proper site characterization, the adoption of a single PSD to represent all runoff conditions may result in SCMs that are under- or over-sized, rendering them ineffective or unnecessarily costly.

Comparative Study for the Standardization of Grinding Equipment During Dry Grinding Process by Various Grinding Mills

The study of grinding behavior characteristics on the metal powders has recently gained scientific interest due to their useful applications to enhance advanced nano materials and components. This could significantly improve the property of new mechatronics integrated materials and components. So, a new evaluation method for standardizing grinding equipment and a comparative study for the grinding experiment during the grinding process with various grinding mills were investigated. The series of grinding experiments were carried out by a traditional ball mill, stirred ball mill, and planetary ball mill with various experimental conditions. The relationship between the standardization of equipment and experimental results showed very significant conclusions. Furthermore, the comparative study on the grinding experiment, which investigated changes in particle size, particle morphology, and crystal structure of materials with changes in experimental conditions for grinding equipment, found that the value of particle size distribution is related to the various experimental conditions as a revolution speed of grinding mill and media size.

Ejecta from experimental impact craters: Particle size distribution and fragmentation energy

The particle size distribution (PSD) of impact crater ejecta is an important parameter that is useful for understanding the formation of natural craters, the distribution of space debris, the influence of impact events on climate and energy partitioning in impact events. 11 impact experiments into dry and water-saturated sandstone were performed and analyzed. The experiments span a range of impact velocities from 2.5 to 5.3kms−1 using projectile sizes from 2.5 to 12mm. Kinetic impact energies between 874 and 80,338J were achieved. Ejecta of these experiments was collected and the PSD was measured and quantified with power law fits. The resulting power law exponents lie between 2.54 and 2.74. Our results do not show an influence of impact energy or impact velocity on the PSD of impact ejecta. A significant increase in the PSD values was found from dry to water-saturated sandstone targets. We suggest that water saturation of the target has multiple effects on ejecta fragmentation. A comparison of our experimental data with data from the literature shows no correlation between the target material lithology and the ejecta PSD. Interestingly, literature data for disruption experiments revealed a strong influence imparted energy density on the D-values. PSD values were used to calculate the energy spent for target fragmentation and show that the fraction of impact energy used for comminution is in the lower single-digit percentage.

Physicochemical properties and skin penetration in vitro of total alkaloids of Sophora flavescens nanoemulsion

The research aimed at investigating the physicochemical properties, stability and skin penetration in vitro of total alkaloids of Sophora flavescens nanoemulsion. Prepare total alkaloids of S. flavescens nanoemulsion and detect the determination of matrine and oxymatrine in the nanoemulsion using HPLC method. Transmission electron microscopy and laser particle size analyzer were utilized to detect the shape and size of the nanoemulsion respectively. And also the stability of nanoemulsion was studied under the conditions of low temperature (4 degrees C), normal temperature (25 degrees C) and high temperature (60 degrees C). Franz diffusion cell was used to research the transdermal absorption of nanoemulsion in vitro. The results found that the nanoemulsion we prepared presented appearance of rounded, uniform; its average diameter was (15.55 +/- 2.24) nm, and particle size distribution value was 0. 161; the appearance, diameter and percentage determination of total alkaloids of S. flavescens had no variations after 15 d under 4, 25, 60 degrees C respectively. The steady-state permeation rate was 4.564 1 microg x cm(-2) x h(-1), 24 h cumulative amount of penetration was 110.7 microg x cm(-2), which was 1.86 fold of 24 h cumulative amount of aqueous solution (59.41 microg x cm(-2)). All the results demonstrated total alkaloids of S. flavescens nanoemulsion had good permeability, and could provide a new preparation for its clinical application.

Improved technique of retrieving particle size distribution from angular scattering measurements

The paper presents results of the simulation study on improved technique of retrieving the particle size distribution (PSD) of dispersed systems from angular scattering measurements. Determining the PSD based on angular scattering measurements is the inverse problem which can be expressed in terms of the Fredholm integral equation of the first kind when single and incoherent scattering modeled by Mie theory is assumed. However, the problem is highly ill-conditioned when discretized. When one incorporates two constraints to be satisfied by the sought PSD: nonnegativity of PSD values and normalization of PSD to unity when integrated over the whole range of particle size into the Regularized Least Squares (RLS) method, one obtains the proposed Constrained Regularized Least Squares (CRLS) method which consists in solving the quadratic programming problem. Accuracy (bias) and uncertainty of the CRLS solutions were assessed in the study. The study refers to the one similar for spectral extinction measurements performed before. Results of the simulation sensitivity study prove that the CRLS method is capable of retrieving PSD functions with accuracy and uncertainty satisfactory for many industrial applications. However, the method does not manage to reconstruct bimodal PSD functions so that both modes are distinguishable. Retrieved PSD satisfies physical constraints inherently.

Simulation research on improved regularized solution of the inverse problem in spectral extinction measurements

We present further results of the simulation research on the constrained regularized least squares (CRLS) solution of the ill-conditioned inverse problem in spectral extinction (turbidimetric) measurements, which we originally presented in this journal [Appl. Opt. 49, 4591 (2010)]. The inverse problem consists of determining the particle size distribution (PSD) function of a particulate system on the basis of a measured extinction coefficient as a function of wavelength. In our previous paper, it was shown that under assumed conditions the problem can be formulated in terms of the discretized Fredholm integral equation of the first kind. The CRLS method incorporates two constraints, which the PSD sought will satisfy: nonnegativity of the PSD values and normalization of the PSD to unity when integrated over the whole range of particle size, into the regularized least squares (RLS) method. This leads to the quadratic programming problem, which is solved by means of the active set algorithm within the research. The simulation research that is the subject of the present paper is a continuation and extension of the research described in our previous paper. In the present research, the performance of the CRLS method variants is compared not only to the corresponding RLS method variants but also to other regularization techniques: the truncated generalized singular value decomposition and the filtered generalized singular value decomposition, as well as nonlinear iterative algorithms: The Twomey algorithm and the Twomey-Markowski algorithm. Moreover, two methods of selecting the optimum value of the regularization parameter are considered: The L-curve method and the generalized cross validation method. The results of our simulation research provide even stronger proof that the CRLS method performs considerably better with reconstruction of PSD than other inversing methods, in terms of better fidelity and smaller uncertainty.

Improved regularized solution of the inverse problem in turbidimetric measurements

We present results of simulation research on the constrained regularized least-squares (RLS) solution of the ill-conditioned inverse problem in turbidimetric measurements. The problem is formulated in terms of the discretized Fredholm integral equation of the first kind. The inverse problem in turbidimetric measurements consists in determining particle size distribution (PSD) function of particulate system on the basis of turbidimetric measurements. The desired PSD should satisfy two constraints: nonnegativity of PSD values and normalization of PSD to unity when integrated over the whole range of particle size. Incorporating the constraints into the RLS method leads to the constrained regularized least-squares (CRLS) method, which is realized by means of an active set algorithm of quadratic programming. Results of simulation research prove that the CRLS method performs considerably better with reconstruction of PSD than the RLS method in terms of better fidelity and smaller uncertainty.