Online estimation of coarse particle-size distributions

In this investigation a technique based on image analysis and numerical transformation has been developed for the on-line sieve size measurement of coarse particles. An advanced image analyzer (the Kontron IBAS II system) was used to obtain the measurement of the linear intercept length distribution (LID) from particle projections. These measurements can be made on-line on particles moving on a conveyor belt. The image processing techniques employed here can improve the quality of the obtained images and filter out the overlapped particles. A measurement of the LID in length is the output of the image analyzer. A normalized unit transformation function was also obtained experimentally for the LID of monosize particles.; A study on the geometrical probability and statistical stereology gives a mathematical model to relate the linear intercept length measurement to the corresponding sieve size distribution of the particles. This stochastic model can incorporate real situations such as polydispersion, irregular shape, and measurement on projections of the particles. A minor assumption on the invariation of a specific particle shape parameter was made and tested to be valid for this case.; The particle size distribution cannot be easily converted from the transformation integral equation due to the measurement error of the LID and the ill-conditioned characteristics of the transformation. A numerical method using physical constraints on the smoothness of size distribution, the nonnegativity, and the consistency of the summation of all size fractions was developed and it solves the problem in least-squares fashion. This new method can eliminate the instabilities and negative values that happened with other methods and can provide improved estimations of the particle size distributions.; Experimental verification of the proposed procedure has been done on both batch and on-line fashions for several test samples. The results show that this method is reliable, and satisfactory estimations of the sieve size measurements can be obtained.