武煜坤， 李政权， 张博群， 陈慧敏， 王贻得， 李凯旋， 李明周

江西理工大学 颗粒技术江西省重点实验室， 江西 赣州 341000

引用格式：

武煜坤，李政权，张博群，等.综合多目标优化和多准则决策的搅拌过程模拟［J］.中国粉体技术，2025，31（2）：1-17.

WU Yukun，LI Zhengquan，ZHANG Boqun，et al.Simulation of mixing process based on integrated multi-objective optimization and multi-crite-ria decision making［J］. China Powder Science and Technology， 2025， 31（2）： 1−17.

DOI：10.13732/j.issn.1008-5548.2025.02.002

收稿日期：2024-06-07， 修回日期：2024-08-27，上线日期：2024-11-21。

基金项目：国家自然科学基金项目，编号：52364047；江西省自然科学基金项目，编号：20212BAB204026。

第一作者简介：武煜坤（1998—），男，硕士生，研究方向为化工机械智能调控。E-mail：1762696883@qq.com。

通信作者简介：李政权（1982—），男， 副教授，博士，硕士生导师，江西省科技领军人才，研究方向为多相流仿真模拟。E-mail：qqzhengquan@163.com。

摘要：【目的】基于已开发的计算流体力学（computational fluid dynamics，CFD）-人工神经网络（artificial neural network，ANN）数据预测模型，利用反映不同决策者偏好的多准则决策方法，针对性地解决搅拌釜在不同工业应用中能耗和搅拌效率的均衡需求和特定偏好需求问题。【方法】利用第二代非支配排序遗传算法（non-dominated sorting genetic algorithmⅡ，NSGA Ⅱ）对CFD-ANN数据预测模型的预测结果进行优化，得到Pareto解集。分别通过熵权法和主观权重对各变量的影响分析确定目标权重占比，并针对不同工业应用场景，利用多准则决策从Pareto解集中选择相应的最优解。【结果】通过优化均衡最优解Opt1，与基础案例Base case相比，能耗降低52. 49%，流体混合程度提升1. 35%，悬浮均匀性提高72. 31%。偏好功率准数N p 的最优解降低功耗86. 5%，偏好流量准数N q 的最优解达到Pareto解集中的理想状态，偏好σ的最优解将固体浓度标准差降低至Base case的9. 93%的同时也优化了能耗。 【结论】本文中提出的基于决策者偏好的多准则决策方法在平衡多个相互冲突的目标方面是有效的。

关键词： 搅拌釜； 计算流体力学； 人工神经网络； 第二代非支配排序遗传算法； 优劣解距离法

Abstract

Objective　In optimizing the design of stirred tanks，the difficulty lies in the variability of structural parameters，operating condi-

tions，and constraints among them.Enhancing performance in one aspect may sacrifice the efficiency of others，making it difficult to     achieve systematic optimization and increasing design costs.Striking a balance between maximizing stirring efficiency and minimizing energy  consumption is a major challenge in the optimization of stirred tank operation. Based on the developed computational fluid dynamics-artificial neural network （CFD-ANN） data prediction model，a multi-criteria decision-making method that reflects different decision-makers’preferences is used to address the challenge in balancing energy consumption and stirring efficiency of stirred tanks in different  industrial applications.

Methods　The CFD-ANN data prediction model was optimized using non-dominated sorting genetic algorithm II（NSGA II）to obtain the Pareto solution set.The target weight ratio was determined by analyzing the influence of each variable through the entropy weight method and su-bjective weighting.The corresponding optimal solution was selected from the Pareto solution set for different industrial application      scenarios using multi-criteria decision making approach.

Results and Discussion　Compared with the Base case，the balanced optimal solution（Opt1）reduced energy consumption by 52.49%，incre-ased fluid mixing by 1.35%，and improved suspension uniformity by 72.31%.Decision-makers significantly improved the performance of stirr-ed tanks by adjusting subjective weights，thereby influencing the selection of optimization solutions.To ensure industrial standards in  key stirred tank parameters，increasing impeller speed and reducing baffle width were recommended.An impeller diameter of 2T/3 with a he-ight of H/4 from the bottom optimized energy-saving，an impeller diameter of T/2.13 with a height of H/6 enhanced uniform fluid mixing， and an impeller diameter of T/1.94 with a height between H/5-H/6 promoted uniform particle suspension. Among the preferred optimal solut-ions based on different industrial application scenarios，when decision-makers prioritized energy saving，an excessively large subjective weight for power number N p（w =［0.70 0.15 0.15］）had a severe impact on other goals.When the subjective weight of N p was 0.4，the pr-oposed solution could reduce energy consumption by 86.5% on average，increasing fluid mixing by 27. 8% and maintaining solid particle suspension uniformity within the required σ.When decision-makers preferred optimal fluid mixing，the proposed scheme reached an ideal N q  in the Pareto solution set，with a value of 0.234 76.It was worth noting that when the optimal fluid dispersion was preferred，a uniform suspension of solid particles could also be achieved under the effect of fluids，yielding an excellent standard deviation of solid conce-ntration of 0.0871 1.Compared to the Base case，this scheme showed superiority in improving fluid dispersion characteristics  within the tank and the upward transport capability for solid particles.When decision-makers preferred a more uniform solid suspension，the proposed solution，though not outstanding in terms of optimizing energy consumption and fluid mixing，still achieved significant improvements of 54.45% and 33.49% in these two performance indicators compared to the Base case，with the standard deviation of solid concentration reduc-ed to 9.93% of the Base case，showing relatively superior performance.It was worth noting that the N p under this preference did not rea-ch the maximum value in the Pareto solution set，indicating that the system performed well in balancing energy consumption and uniform   mixing of solid particles.

Conclusion　The study，based on a multi-objective optimization model， investigates the impact of varying subjective weights on various dependent variables.It finely controls N p ，N q ，and σ in stirred tanks based on different decision-making preferences to obtain opti-mal solutions that meet specific needs.The performance of each preferred optimal solution is evaluated.A new method is introduced to bal-ance multiple conflicting objectives in stirred tank optimization，and corresponding optimal solutions are proposed based on different   decisions.It provides theoretical support and reference for stirred tank performance optimization and industrial production.

Keywords： stirred tank； computational fluid dynamics； artificial neural network； non-dominated sorting genetic algorithm II；

technique for order preference by similarity to ideal solution

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