Chance constrained optimization for copper removal process under uncertainty in zinc hydrometallurgy

doi:10.11949/0438-1157.20191494

Abstract

Abstract:

Copper removal process(CRP) is an important step in hydrometallurgical zinc process. Due to the changeable production conditions, diverse mineral resources and complex mechanisms, there exist uncertainties in the process of copper removal, which affect the stability and reliability of production. In this paper, the chance constrained optimization for the copper removal process under uncertainty is studied, considering the uncertainty of the inlet flow rate, the returned underflow rate and the inlet copper ions concentration. Firstly, the uncertainties of the copper removal process are analyzed, and the distribution characteristics of the uncertain parameters are analyzed by using statistical methods. The idea of chance constraint is introduced, and the problem of the copper removal process under uncertain conditions is formulated as a chance constrained optimization problem. Then the chance constrained optimization problem is transformed into a nonlinear programming problem by the back-mapping approach(BMA). Finally, sequential quadratic programming is used to solve the resulting problem. Monte Carlo simulation verify the effectiveness of the proposed method and demonstrate that the robustness of the system is significantly improved.

Key words: process control, nonlinear dynamics, Monte Carlo simulation, copper removal process, uncertain optimization, chance constrained optimization

摘要：

除铜过程是湿法炼锌净化工艺中的重要步骤，受生产环境多变、矿源多样、机理复杂等因素的影响，除铜过程存在不确定性，影响生产的稳定性和可靠性。针对除铜过程中入口溶液流量、底流返回量和入口铜离子浓度的不确定性，造成出口铜离子浓度不稳定的问题，研究不确定条件下的除铜过程机会约束优化控制方法。首先分析了除铜过程的不确定性，利用统计学方法分析不确定参数的分布特性，引入了机会约束的思想，将不确定条件下的除铜过程优化问题建模为机会约束优化问题。然后采用可行域映射方法，将机会约束优化问题转化为非线性规划问题。最后，使用序列二次规划求解该非线性规划问题。Monte Carlo仿真验证了该方法的有效性，可以提高系统的鲁棒性。

关键词: 过程控制, 非线性动力学, Monte Carlo模拟, 除铜过程, 不确定优化, 机会约束优化

CLC Number:

TP 273

Xiangyue WANG, Xiaojun ZHOU, Chunhua YANG. Chance constrained optimization for copper removal process under uncertainty in zinc hydrometallurgy[J]. CIESC Journal, 2020, 71(3): 1226-1233.

王湘月, 周晓君, 阳春华. 不确定条件下的湿法炼锌除铜过程机会约束优化控制[J]. 化工学报, 2020, 71(3): 1226-1233.

Figures/Tables 6

Fig.1 Flow diagram of CRP

Fig.2 Histogram of inlet solution flow rate

Fig.3 Normal probability plot of inlet solution flow rate

Fig.4 Flowchart of BMA

Table 1 Comparison of back-mapping approach(BMA) and expectation optimization method(EOM) of results

α/%	u₁/(kg/h)		u₂/(kg/h)		J		计算时间/s		Monte Carlo模拟结果/%
α/%	BMA	EOM	BMA	EOM	BMA	EOM	BMA	EOM	BMA	EOM
65	81.1	66.6	79.1	65.7	320.4	264.6	0.2	0.02	65.07	48.18
70	142.2	66.6	45.3	65.7	375.0	264.6	0.4	0.02	70.02	48.18

Fig.5 Monte Carlo simulation result

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