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摘要: 针对城市污水处理过程的非线性、不确定性以及非高斯等特点, 提出一种数据驱动的溶解氧(Dissolved oxygen, DO)浓度在线自组织控制方法. 首先, 设计一种基于相关熵的自组织模糊神经网络控制器(Correntropy-based self-organizing fuzzy neural network, CSOFNN), 采用相关熵与规则贡献度指标实现控制器结构与参数的自动构建或修剪. 其次, 设计基于相关熵诱导准则的补偿控制器及参数自适应律, 充分利用相关熵抑制非高斯噪声的能力, 能够有效地降低系统中的不确定性. 然后, 分析所提出的控制方法的稳定性, 从而保证其在实际应用中的可靠性. 最后, 基于基准仿真1号模型(Benchmark simulation model No. 1, BSM1)的实验验证了所提方法的有效性.Abstract: To deal with the nonlinearity, uncertainty and non-Gaussianity of urban wastewater treatment processes, this paper proposes a data-driven online self-organizing control method for dissolved oxygen (DO). First, a correntropy-based self-organizing fuzzy neural network (CSOFNN) controller is designed. For CSOFNN, its structure and parameters can be automatically generated or pruned based on the correntropy and rules-contribution indexes. Second, the compensation controller and parameter adaptive laws are developed using the correntropy-induced criterion, thus can tackle non-Gaussian noise and reduce the system uncertainty. Third, the stability of the proposed control method is analyzed theoretically, thus ensuring its feasibility in practice. Finally, the proposed control method is tested in the benchmark simulation model No. 1 (BSM1). The experimental results show its effectiveness.
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图 1 A/O工艺城市污水处理流程图
Fig. 1 Schematic diagram of urban wastewater treatment with the A/O process
图 2 基于CSOFNN的溶解氧浓度控制系统框图
Fig. 2 Diagram of the CSOFNN-based control system for the DO concentration
图 4 恒定So下CSOFNN控制器规则变化曲线
Fig. 4 Rules variations of CSOFNN controller under constant So
图 8 变So下CSOFNN控制器规则变化曲线
Fig. 8 Rules variations of CSOFNN controller under variable So
表 1 恒定So时不同控制器的性能比较
Table 1 Performance comparisons of different controllers under constant So
干扰类型 控制器 规则数 $IAE $ $ISE $ $Dev^{\max}$ 连续降雨 CSOFNN 4 2.1×10−3 3.00×10−6 7.44×10−3 CFNN[19] 6* 3.2×10−3* 8.76×10−6* 7.56×10−3* SOFC[15] 10* 3.1×10−2* 7.26×10−4* 3.6×10−2* SOFNN[20] 12* 4.2×10−2* 1.81×10−4* 1.12×10−2* 突发暴雨 CSOFNN 4 1.9×10−3 1.44×10−6 3.42×10−3 CFNN[19] 6* 2.1×10−3* 1.75×10−6* 3.46×10−3* SOFC[15] 9* 2.5×10−2* 8.63×10−4* 9.7×10−2* SOFNN[20] 12* 6.0×10−2* 1.19×10−3* 8.22×10−2* 注: * 表示原文中的结果, 粗体表示最好的结果. 
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表 2 变So下不同控制器的性能比较
Table 2 Performance comparisons of different controllers under variable So
干扰类型 控制器 规则数 $IAE $ $ISE $ $Dev^{\max}$ 降雨 CSOFNN 5 2.4×10−3 1.67×10−4 7.14×10−3 CFNN[19] 6* 2.1×10−3* 2.34×10−4* 7.60×10−3* SOFC[15] 14* 2.2×10−2* 2.86×10−4* 3.5×10−2* SOTSFNN[20] 9* 0.48* 9.7×10−4* 1.0×10−2* 降雨 + 脉冲噪声 CSOFNN 6 4.8×10−3 3.41×10−4 2.02×10−2 CFNN[19] 6 3.63×10−2 1.11×10−3 3.22×10−2 SOFC[15] 10 4.49×10−2 9.97×10−4 3.62×10−2 SOTSFNN[20] 20 1.33 2.47×10−2 4.29×10−2 注: * 表示原文中的结果, 粗体表示最好的结果.
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