Entropy-based estimation of bubble size distributions in froth flotation using B-spline functions

Abstract: Bubble size distribution is an important feature in froth flotation processes and the B-spline estimation is a common way to approximate the bubble size distribution by using the least square algorithm. However, it is difficult to determine the number of basis functions of B-spline. In this study, the analysis based on the unbiased cross entropy is proposed to evaluate the estimated models. Experimental results have shown the feasibility and effectiveness of the proposed method.

[1]  Weihua Gui,et al.  Nonparametric density estimation of bubble size distribution for monitoring mineral flotation process , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[2]  Chunhua Yang,et al.  Bubble size estimation using interfacial morphological information for mineral flotation process monitoring , 2009 .

[3]  Chris Aldrich,et al.  The significance of flotation froth appearance for machine vision control , 1996 .

[4]  Silvia Serranti,et al.  Characterization of the flotation froth structure and color by machine vision (ChaCo) , 2000 .

[5]  Stephen J. Neethling,et al.  The relationship between the surface and internal structure of dry foam , 2009 .

[6]  Hong Wang,et al.  Filter‐based fault detection and diagnosis using output PDFs for stochastic systems with time delays , 2006 .

[7]  Weixing Wang,et al.  Image analysis and computer vision for mineral froth , 2005, IEEE International Conference Mechatronics and Automation, 2005.

[8]  Weihua Gui,et al.  Probability density function of bubble size based reagent dosage predictive control for copper roughing flotation , 2014 .

[9]  Wu Ji Mineral concentration estimation of feed ore in gold and stibium flotation based on froth image features , 2015 .

[10]  Giuseppe Bonifazi,et al.  Characterisation of flotation froth colour and structure by machine vision , 2001 .

[11]  W. Wang,et al.  Froth delineation based on image classification , 2003 .

[12]  John F. MacGregor,et al.  Flotation froth monitoring using multiresolutional multivariate image analysis , 2005 .

[13]  Sten Bay Jørgensen,et al.  Bubble Size Estimation for Flotation Processes , 2008 .

[14]  Franklin A. Graybill,et al.  Introduction to the Theory of Statistics, 3rd ed. , 1974 .

[15]  K. Lam,et al.  Estimation of complicated distributions using B-spline functions , 1998 .

[16]  Chris Aldrich,et al.  The effect of mothers on bubble size distributions in flotation pulp phases and surface froths , 2000 .

[17]  Hong Wang,et al.  Optimal probability density function control for NARMAX stochastic systems , 2008, Autom..