Probability density function of bubble size based reagent dosage predictive control for copper roughing flotation

Abstract

As an effective measurement indicator of bubble stability, bubble size structure is believed to be closely related to flotation performance in copper roughing flotation. Moreover, reagent dosage has a very important influence on the bubble size structure. In this paper, a novel reagent dosage predictive control method based on probability density function (PDF) of bubble size is proposed to implement the indices of roughing circuit. Firstly, the froth images captured in the copper roughing are segmented by using a two-pass watershed algorithm. In order to characterize bubble size structure with non-Gaussian feature, an entropy based B-spline estimator is hence investigated to depict the PDF of the bubble size. Since the weights of B-spline are interrelated and related to the reagent dosage, a multi-output least square support vector machine (MLS-SVM) is applied to establish a dynamical relationship between the weights and the reagent dosage. Finally, an entropy based optimization algorithm is proposed to determine reagent dosage in order to implement tracking control for the PDF of the output bubble size. Experimental results can show the effectiveness of the proposed method.

Soft computing-based modeling of flotation processes – A review

“…Examples include: particle swarm optimization (Leng et al, 2010;Tian and Yang, 2014;Zhu et al, 2013;Wang et al, 2014b;Wang and Han, 2015), glowworm swarm optimization (Wang et al, , 2014b, gravitational search algorithm (Massinaei et al, 2011(Massinaei et al, , 2013Wang and Han, 2015), differential evolution (Aldrich et al, 2000;Leng et al, 2010;Cao et al, 2013Cao et al, , 2014, artificial immune systems (Yong et al, 2012;Xiaoping and Aldrich, 2013), and cuckoo searching algorithm (Wang et al, 2014a). Almost as a rule, the application of these methods is related to the optimization of flotation models parameters.…”

“…FL GA SVM FL Shahbazi et al (2013), Sheng and Wen (2013), Li et al (2013), Wang and Zhang (2006) Other Lima (1997, 1998), Gupta et al (1999), ElShall et al (2001), Rughooputh and Rughooputh (2002), Zhu and Wang (2008), Zimmermann and Jeanmeure (1996) Zhu et al (2013), Cao et al (2013), and Yang and Huang (2010a,b) …”

“…25. Concentrate grade and recovery with (afternoon shift) and without proposed predictive control structure (morning and night shifts) (adapted fromZhu et al, 2013).Fig. 26.…”

Predictive PDF control in shaping of molecular weight distribution based on a new modeling algorithm

“…Like MWD control in polymerization processes, many other industrial processes also have the problems that the product quality to be controlled is closely linked to output variables that need to follow certain distribution patterns, for example, particle size distribution (PSD) control in polymerization processes [13][14][15][16], pulp fibre length distribution control in paper industries [17], particulate process control in powder industries [18,19], crystal size distribution (CSD) control in crystallization processes [20][21][22], crystal size and shape distribution control of protein crystal aggregation in biopharmaceutical production [23], flame temperature distribution control in furnace systems [24,25], power PDF control in nuclear research reactors [26], and bubble size distribution control in flotation processes [27], to name a few. To tackle the control problems for such systems, the idea of output stochastic distribution control (SDC) or output PDF control has been proposed, in which the full shape of the output distribution is directly controlled [28][29][30][31][32].…”

The Method of Reagent Control Based on Time Series Distribution of Bubble Size in a Gold‐Antimony Flotation Process

“…12 ⋯ a 1n a 21 a 22 ⋯ a 2n is the value of the projection vector that reflects the data feature of multi-dimensional a(m × n) in one-dimensional space.…”