Particle size distribution of coarse aggregates through mechanical sieving gives results in terms of cumu- lative mass percent. But digital image processing generated size distribution of particles, while being fast a...Particle size distribution of coarse aggregates through mechanical sieving gives results in terms of cumu- lative mass percent. But digital image processing generated size distribution of particles, while being fast and accurate, is often expressed in terms of area function or number of particles. In this paper, a mass model is developed which converts the image obtained size distribution to mass-wise distribution, mak- ing it readily comparable to mechanical sieving data. The concept of weight/particle ratio is introduced for mass reconstruction from 2D images of particle aggregates. Using this mass model, the effects of several particle shape parameters （such as major axis, minor axis, and equivalent diameter） on sieve-size of the particles is studied. It is shown that the sieve-size of a particle strongly depend upon the shape param- eters, 91% of its variation being explained by major axis, minor axis, bounding box length and equivalent diameter. Furthermore, minor axis gives an overall accurate estimate of particle sieve-size, error in mean size （D-50） being just 0.4%. However, sieve-size of smaller particles （〈20 ram） strongly depends upon the length of the smaller arm of the bounding box enclosing them and sieve-sizes of larger particles （〉20 mm） are highly correlated to their equivalent diameters. Multiple linear regression analysis has been used to generate overall mass-wise particle size distribution, considering the influences of all these shape parameters on particle sieve-size. Multiple linear regression generated overall mass-wise particle size distribution shows a strong correlation with sieve generated data. The adjusted R-square value of the regression analysis is found to be 99 percent （w.r,t cumulative frequency）. The method proposed in this paper provides a time-efficient way of producing accurate （up to 99%） mass-wise PSD using digital image processing and it can be used effectively to renlace the mechanical sieving.展开更多
Instead of most existing postprocessing schemes, a new preprocessing approach, called multi- neighboring grids （MNG）, is proposed for solving PDE eigen-problems on an existing grid G（A）. The linear or multi-linear...Instead of most existing postprocessing schemes, a new preprocessing approach, called multi- neighboring grids （MNG）, is proposed for solving PDE eigen-problems on an existing grid G（A）. The linear or multi-linear element, based on box-splines, are taken as the first stage Khuh -λh/1Mh/1Uh. In this paper, the j-th stage neighboring-grid scheme is defined as Khuh λh/j Mh/j Uh = λh/j Mh/j Uh , where gh ：- Mh/j-1 Kh/1 and Mhuh is to be found as a better mass distribution over the j-th stage neighboring-grid G（/k）, and Kh/1 can be seen as an expansion of Kh on the j-th neighboring-grid with respect to the （j - 1）-th mass distribution Mh_l. It is shown that for an ODE model eigen-problem, the j-th stage scheme with 2j-th order B-spline basis can reach 2j-th order accuracy and even （2j ＋ 2）-th order accuracy by perturbing the mass matrix. The argument can be extended to high dimensions with separable variable cases. For Laplace eigen-problems with some 2-D and 3-D structured uniform grids, some 2j-th order schemes are presented for j ≤ 3.展开更多
基金Indian Institute of Technology,Kharagpur in India for supporting this work
文摘Particle size distribution of coarse aggregates through mechanical sieving gives results in terms of cumu- lative mass percent. But digital image processing generated size distribution of particles, while being fast and accurate, is often expressed in terms of area function or number of particles. In this paper, a mass model is developed which converts the image obtained size distribution to mass-wise distribution, mak- ing it readily comparable to mechanical sieving data. The concept of weight/particle ratio is introduced for mass reconstruction from 2D images of particle aggregates. Using this mass model, the effects of several particle shape parameters （such as major axis, minor axis, and equivalent diameter） on sieve-size of the particles is studied. It is shown that the sieve-size of a particle strongly depend upon the shape param- eters, 91% of its variation being explained by major axis, minor axis, bounding box length and equivalent diameter. Furthermore, minor axis gives an overall accurate estimate of particle sieve-size, error in mean size （D-50） being just 0.4%. However, sieve-size of smaller particles （〈20 ram） strongly depends upon the length of the smaller arm of the bounding box enclosing them and sieve-sizes of larger particles （〉20 mm） are highly correlated to their equivalent diameters. Multiple linear regression analysis has been used to generate overall mass-wise particle size distribution, considering the influences of all these shape parameters on particle sieve-size. Multiple linear regression generated overall mass-wise particle size distribution shows a strong correlation with sieve generated data. The adjusted R-square value of the regression analysis is found to be 99 percent （w.r,t cumulative frequency）. The method proposed in this paper provides a time-efficient way of producing accurate （up to 99%） mass-wise PSD using digital image processing and it can be used effectively to renlace the mechanical sieving.
基金supported by National Natural Science Foundation of China(Grant Nos.6097008961170075 and 91230109)
文摘Instead of most existing postprocessing schemes, a new preprocessing approach, called multi- neighboring grids （MNG）, is proposed for solving PDE eigen-problems on an existing grid G（A）. The linear or multi-linear element, based on box-splines, are taken as the first stage Khuh -λh/1Mh/1Uh. In this paper, the j-th stage neighboring-grid scheme is defined as Khuh λh/j Mh/j Uh = λh/j Mh/j Uh , where gh ：- Mh/j-1 Kh/1 and Mhuh is to be found as a better mass distribution over the j-th stage neighboring-grid G（/k）, and Kh/1 can be seen as an expansion of Kh on the j-th neighboring-grid with respect to the （j - 1）-th mass distribution Mh_l. It is shown that for an ODE model eigen-problem, the j-th stage scheme with 2j-th order B-spline basis can reach 2j-th order accuracy and even （2j ＋ 2）-th order accuracy by perturbing the mass matrix. The argument can be extended to high dimensions with separable variable cases. For Laplace eigen-problems with some 2-D and 3-D structured uniform grids, some 2j-th order schemes are presented for j ≤ 3.
