粒子群优化算法波阻抗反演

Improved particle swarm impedance inversion

粒子群算法比较简单、容易操作,对求解高维度问题有较好的优势,但存在2个问题:1)常规的粒子群算法信息间的交流是通过自身解与全局最优解间交流得到,群体内部交流过少;2)常规的线性惯性权重作用过于单一,不利于反演后期结果的快速收敛。文中提出的粒子群优化算法,以粒子群理论为核心,遗传优化算法引进交叉算法,修改惯性权重,提供的随机游走步长逐渐变小,在目标函数及初始模型的约束下,缓慢地缩小步长,以求先快速跳出局部极值,然后不断减小步长,靠近最优值。通过分析粒子群原理、遗传核心理论,详细分析粒子群参数,优选参数,并将其同传统的算法相比较,优选算法,随后,进行抗噪性及模型试验。分析发现,噪声含量比在30%之内时反演结果与实际吻合,模型反演结果在初始模型上有所改进。这证明该方法在实际反演中是实用可行的。

PSO（Particle Swarm Optimization） provides a relatively simple operation to solve the high-dimensional problem with distinct advantages.But there are two problems remaining： the information communication in conventional PSO indicates the communications between the best known solution in searching space and optimal solution,which leads to inadequate communications within the group; the conventional linear inertia weight function is excessively single,which is not sufficient for the forward convergence of the inversion results.Based on PSO theory and cross operator in genetic algorithm,the particle swarm optimization algorithm proposed in this paper modified the inertia weight with variance-diminishing random steps.Under the constraints of initial model of objective function,slowly narrowing steps can help to quickly jump out of local minima and get close to optimal solution.Through the analysis of PSO theory and GA（genetic algorithms） method,each parameter is analyzed and optimized in detail.After the comparison with conventional PSO method,further validation and test were conducted,such as noise immunity test and numerical model test.The analysis result shows the inversion results are consistent with actual data with noise level under 30%.And the hybrid method presents a better result than conventional method.It can be concluded that this new hybrid method is robust and feasible.