Nonparametric density estimation of froth colour texture distribution for monitoring sulphur flotation process

• A completer texture description method called CTD is proposed considering colour variation.
• The fixed kernel basis proposed to estimate CTD can compare different flotation performance.
• The Schmidt orthogonalisation theory realises the sparseness effectively and rapidly in LS-SVM.
• The multiple-kernel in LS-SVM obtains excellent local learning and global generalization ability.

As an important indicator of flotation performance, froth texture is believed to be related with operational condition in sulphur flotation process. A novel froth images classification method based on froth colour texture unit distribution is proposed to recognise different performance of sulphur flotation in real time. The froth colour texture unit number is calculated by using colour value instead of grey level value in texture unit number, and the probability density function of froth colour texture unit number is defined as colour texture distribution, which can describe the actual textual feature more completely than traditional texture description approach. As the type of the froth colour texture distribution is unknown, a nonparametric kernel estimation method based on the fixed kernel basis is proposed. It is impossible to use the traditional varying kernel basis to compare different colour texture distributions under various conditions while the proposed fixed kernel basis can overcome the difficulty. Through transforming nonparametric description into dynamic kernel weight vector, the combination of normal kernel with polynomial kernel based sparse multiple-kernel least square support vector machine classifiers are constructed to realise the performance classification. Furthermore, the kernel matrices are reduced by Schmidt orthogonalisation theory to lower the computational complexity. The industrial application results show that the accurate performance classification of sulphur flotation can be achieved by using the proposed method.