Information about size and shape of particles produced in various manufacturing processes is very important for process and product development because design of downstream processes as well as final product properties strongly depend on these geometrical particle attributes. However, recovery of particle size and shape information in situ during crystallisation processes has been a major challenge. The focused beam reflectance measurement (FBRM) provides the chord length distribution (CLD) of a population of particles in a suspension flowing close to the sensor window. Recovery of size and shape information from the CLD requires a model relating particle size and shape to its CLD as well as solving the corresponding inverse problem.This paper presents a comprehensive algorithm which produces estimates of particle size distribution and particle aspect ratio from measured CLD data. While the algorithm searches for a global best solution to the inverse problem without requiring further a priori information on the range of particle sizes present in the population or aspect ratio of particles, suitable regularisation techniques based on relevant additional information can be implemented as required to obtain physically reasonable size distributions. We used the algorithm to analyse CLD data for samples of needle-like crystalline particles of various lengths using two previously published CLD models for ellipsoids and for thin cylinders to estimate particle size distribution and shape. We found that the thin cylinder model yielded significantly better agreement with experimental data, while estimated particle size distributions and aspect ratios were in good agreement with those obtained from imaging

Efficient processing of particulate products across various manufacturing steps requires that particles possess desired attributes such as size and shape. Controlling the particle production process to obtain required attributes will be greatly facilitated using robust algorithms providing the size and shape information of the particles from in situ measurements. However, obtaining particle size and shape information in situ during manufacturing has been a big challenge. This is because the problem of estimating particle size and shape (aspect ratio) from signals provided by in-line measuring tools is often ill posed, and therefore it calls for appropriate constraints to be imposed on the problem. One way to constrain uncertainty in estimation of particle size and shape from in-line measurements is to combine data from different measurements such as chord length distribution (CLD) and imaging. This paper presents two different methods for combining imaging and CLD data obtained with in-line tools in order to get reliable estimates of particle size distribution and aspect ratio, where the imaging data is used to constrain the search space for an aspect ratio from the CLD data

Imaging defects in austenitic welds presents a significant challenge for the ultrasonic non-destructive testing community. Due to the heating process during their manufacture, a dendritic structure develops, exhibiting large grains with locally anisotropic properties which cause the ultrasonic waves to scatter and refract. When basic imaging algorithms, which typically make constant wave speed assumptions, are applied to datasets arising from the inspection of these welds, the resulting defect reconstructions are often distorted and difficult to interpret correctly. However, knowledge of the underlying spatially varying material properties allows correction of the expected wave travel times and thus results in more reliable defect reconstructions. In this paper, an approximation to the underlying, locally anisotropic structure of the weld is constructed from ultrasonic time of flight data. A new forward model of wave front propagation in locally anisotropic media is presented and used within the reversible-jump Markov chain Monte Carlo method to invert for the map of effective grain orientations across different regions of the weld. This forward model and estimated map are then used as the basis for an advanced imaging algorithm and the resulting defect reconstructions exhibit a significant improvement across multiple flaw characterization metrics.

Traditional imaging algorithms within the ultrasonic non-destructive testing community typically assume that the material being inspected is primarily homogeneous, with heterogeneities only at sub-wavelength scales. When the medium is of a more generally heterogeneous nature, this assumption can contribute to the poor detection, sizing and characterisation of defects. Prior knowledge of the varying wave speeds within the component would allow more accurate imaging of defects, leading to better decisions about how to treat the damaged component. This work endeavours to reconstruct the inhomogeneous wave speed maps of random media from simulated ultrasonic phased array data. This is achieved via application of the reversible-jump Markov chain Monte Carlo method: a sampling-based approach within a Bayesian framework. The inverted maps are used in conjunction with an imaging algorithm to correct for deviations in the wave speed, and the reconstructed flaw images are then used to quantitatively assess the success of this methodology. Using full matrix capture data arising from a finite element simulation of a phased array inspection of a heterogeneous component, a six-fold improvement in flaw location is achieved by taking into account the reconstructed wave speed map which exploits almost no a priori knowledge

Manufacturing of particulate products across many industries relies on accurate measurements of particle size distributions in dispersions or powders. Laser diffraction (or small angle light scattering) is commonly used, usually off-line, for particle size measurements. The estimation of particle sizes by this method requires the solution of an inverse problem using a suitable scattering model that takes into account size, shape and optical properties of the particles. However, laser diffraction instruments are usually accompanied by software that employs a default scattering model for spherical particles, which is then used to solve the inverse problem even though a significant number of particulate products occur in strongly non-spherical shapes such as needles. In this work, we demonstrate that using the spherical model for the estimation of sizes of needle-like particles can lead to the appearance of artefacts in the form of multimodal populations of particles with size modes much smaller than those actually present in the sample. This effect can result in a significant under-estimation of the mean particle size and in false modes in estimated particles size distributions

Ultrasonic phased array systems have become increasingly popular in the last 10 years as tools for flaw detection and characterization within the nondestructive testing industry. The existence and location of flaws can often be deduced via images generated from the data captured by these arrays. A factor common to these imaging techniques is the subjective thresholding required to estimate the size of the flaw. This paper puts forward an objective approach which employs a mathematical model. By exploiting the relationship between the width of the central lobe of the scattering matrix and the crack size, an analytical expression for the crack length is reached via the Born approximation. Conclusions are then drawn on the minimum resolvable crack length of the method and it is thus shown that the formula holds for subwavelength defects. An analytical expression for the error that arises from the discrete nature of the array is then derived and it is observed that the method becomes less sensitive to the discretization of the array as the distance between the flaw and array increases. The methodology is then extended and tested on experimental data collected from welded austenitic plates containing a lack-of-fusion crack of 6 mm length. An objective sizing matrix (OSM) is produced by assessing the similarity between the scattering matrices arising from experimentally collected data with those arising from the Born approximation over a range of crack lengths and frequencies. Initially, the global minimum of the OSM is taken as the objective estimation of the crack size, giving a measurement of 7 mm. This is improved upon by the adoption of a multifrequency averaging approach, with which an improved crack size estimation of 6.4 mm is obtained.