带扰动算子的量子粒子群在水污染源识别中的应用

Estimation of Contamination Source by Using QPSO with Perturbation Operator

提出一种带扰动算子的量子行为粒子群优化算法,将其用于求解对流-扩散反问题中的估计随时间变化的污染源问题。污染源是时变函数,问题归结为函数估计问题(function estimation problem)。为了将反问题转化为优化问题,我们采用了非线性最小二乘模型。考虑到采样数据可能存在噪声,Tikhonov正则化方法用来取得稳定解,L-curve方法用来求得正则参数。仿真结果表明:带扰动算子的量子粒子群算法明显优于传统量子粒子群算法,能够帮助粒子从局部最优中跳出来。从不同的角度对算法进行了测试(正则项,噪声级别,传感器的位置等)。

An improved quantum-behaved particle swarm optimization(QPSO) with perturbation operator was proposed and applied to solve the convection-diffusion inverse problem of estimating time-varying contamination source. Because the contamination source is time-dependent, the inverse problems are classified into function estimation problem. To transform the inverse problem to optimization problem, the nonlinear least square method was used. Meanwhile, Tikhonov regularization was used to stablize the solution with noisy measured data. And the regularization parameter was chosen by L-curve method. The simulation results tell that QPSO with perturbation operator outperforms QPSO and PSO. Moreover, tests over different views(regularization terms, noise level, sensor positions) were performed.