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 同济大学学报(自然科学版)  2017, Vol. 45 Issue (8): 1198-1203,1208.  DOI: 10.11908/j.issn.0253-374x.2017.08.014 0

### 引用本文

ZENG Lingjie, GAO Jun. Genetic Algorithm for Sudden Contaminant Source Identification in Ventilation System[J]. Journal of Tongji University (Natural Science), 2017, 45(8): 1198-1203,1208. DOI: 10.11908/j.issn.0253-374x.2017.08.014.

### 文章历史

Genetic Algorithm for Sudden Contaminant Source Identification in Ventilation System
ZENG Lingjie, GAO Jun
School of Mechanical Engineering, Tongji University, Shanghai 200092, China
Abstract: This paper illustrated a source identification method in air duct system, aiming at detecting contaminant source within a short period of time after a bio-terrorist attack. The method was based on genetic algorithm (GA) with minimal difference between calculated concentration and measured concentration as fitness function. We established a database of calculated concentration of sensors considering different releasing scenarios. Then we discussed the impact of the number of sensors, the location and measurement time of sensors, the capability of sensors, and the distance between nodes on the overall average relative error of inversion results (ξ). Results of a case study showed that the ξ decreased as more sensors were set in the ventilation system. The optimized number of sensors in this case was supposed three, considering both the decrement provided by each sensor and the high cost of each sensor. Meanwhile, the convergence generations were few while the convergence time was short. Then, the impact of sensor location and detection time on the ξ was coupled. The inversed source location x0 is sensitive to the time interval of feedback data but non-sensitive to the detecting error of sensors. Finally, there existed an appropriate number of nodes distance in air duct system, which gave consideration to lower calculated load and global optimization.
Key words: ventilation system    source identification    sudden contaminant    sensor

1 基于遗传算法的污染溯源模型 1.1 模型的建立

 $\frac{{\partial C}}{{\partial t}}{\rm{ = }}\varepsilon_x\frac{{{\partial ^2}C}}{{\partial {x^2}}}-{u_x}\frac{{\partial C}}{{\partial x}}-KC$ (1)

 $C = \frac{{{M_0}}}{{A\sqrt {4\pi {\varepsilon _x}t} }}\exp \left[{-\frac{{{{\left( {x-{u_x}t} \right)}^2}}}{{4{\varepsilon _x}t}}} \right]\exp \left[{-Kt} \right]$ (2)
 ${\mathit{\boldsymbol{C}}_{\rm{d}}} = {\mathit{\boldsymbol{M}}^{-1}}\mathit{\boldsymbol{f}}$ (3)

 $g\left( I \right) = {\sum\limits_{j = 1}^{{N_{\rm{t}}}} {\sum\limits_{i = 1}^{{N_{\rm{r}}}} {\left[{\frac{{C_{{\rm{cal}}}^i\left( j \right)-C_{{\rm{mes}}}^i\left( j \right)}}{{C_{{\rm{mes}}}^i\left( j \right)}}} \right]} } ^2}$ (4)

1.2 优化变量与约束条件

 $\mathit{\boldsymbol{X}} \in \left( {{\mathit{\boldsymbol{X}}_{{\rm{node }}\;1}},{\mathit{\boldsymbol{X}}_{{\rm{node }}\;2}},{\bf{\cdots}} ,{\mathit{\boldsymbol{X}}_{{\rm{node }}\;n}}} \right)$ (5)
 $\mathit{\boldsymbol{M}} \in \left( {{\mathit{\boldsymbol{M}}_1},{\mathit{\boldsymbol{M}}_2},\cdots ,{\mathit{\boldsymbol{M}}_n}} \right)$ (6)
 $\mathit{\boldsymbol{T}} \in \left( {{\mathit{\boldsymbol{T}}_1},{\mathit{\boldsymbol{T}}_2}, \cdot \cdot \cdot ,{\mathit{\boldsymbol{T}}_n}} \right)$ (7)

1.3 遗传算法求解

 图 1 风系统突发污染溯源算法实现流程 Fig.1 Procedure of sudden contaminant source identification method in ventilation system

 $\xi = \sum\limits_{i = 1}^n {\frac{{\left| {{\pmb{p}_i}-{\pmb{p}_0}} \right|}}{{\left| {{\pmb{p}_0}} \right|}}} /n$ (8)

2 溯源结果及分析 2.1 传感器数目对溯源结果的影响分析

 图 2 设置节点后的风系统示意 Fig.2 Air duct system

 图 3 不同传感器数目对应的传感器优化布置方案 Fig.3 Optimal sensor layouts based on different number of sensors

 图 4 传感器数目对反演结果总平均误差的影响 Fig.4 Impact of sensor quantity on the overall average relative error of inversion results

 图 5 溯源适应度函数收敛情况 Fig.5 Convergence property of inversion calculation
 图 6 反演所需时间内，模型计算的污染物定性影响区域示意 Fig.6 Affect zone of contaminant under model simulation within the required time of inversion
2.2 传感器监测位置、时间及性能对溯源结果影响分析

 图 7 传感器监测位置及首次监测到污染物的时间对反演结果总平均相对误差的影响 Fig.7 Impact of the location and measurement time of sensors on the overall average relative error of inversion results

 图 8 传感器误差及传回数据间隔时间对反演源位置x0影响 Fig.8 Impact of detecting error of sensors and time interval of feedback data on the identification of source location x0
2.3 节点划分对溯源过程的影响分析

3 结论

(1) 针对某一特定风系统，经位置优化后的传感器数目越多，ξ越小，但当风系统中的传感器数目超过3个时，每增加一个传感器，ξ仅降低约3.5%，考虑到单个传感器成本较高，故该风系统内宜设置3个传感器.

(2) 在反演过程中，传感器监测位置与时间是一对耦合的参数，首个监测到污染物的传感器离污染源越远，ξ越大，同时该误差是随传感器首次监测到污染物的时间增长而增大的.而源位置参数x0的反演相对误差与传感器监测误差无关，却随传感器传回数据时间间隔增大而增大.

(3) 当风系统节点总数在适当范围内时，既能在一定程度上减少遗传算法存储数据量，降低运算负荷，又能兼顾在整个风系统内溯源的目的.

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