基于改进蝴蝶优化算法的瑞利波频散曲线反演方法  

An improved butterfly optimization algorithm in the inversion of Rayleigh wave dispersion curve

作　　者：彭刘亚[1] 冯伟栋[1] 解惠婷 李飞 杨源源[1] 曹均锋[1] 任川 PENG Liu-Ya;FENG Wei-Dong;XIE Hui-Ting;LI Fei;YANG Yuan-Yuan;CAO Jun-Feng;REN Chuan(Anhui Earthquake Agency,Hefei 230031,China;Anhui Huizhou Geology Security Institute Co.,Ltd.,Hefei 231202,China)

机构地区：[1]安徽省地震局,安徽合肥230031 [2]安徽惠洲地质安全研究院股份有限公司,安徽合肥231202

出　　处：《物探与化探》2024年第3期705-720,共16页Geophysical and Geochemical Exploration

基　　金：国家自然科学基金项目(41802224);2022年安徽省重点研究与开发计划项目(2022m07020005)。

摘　　要：瑞利波频散曲线反演问题的多解性和反演目标函数的多极值特点,使得常规非线性优化算法可能会产生收敛不稳定、易陷入局部最优等现象。在基本蝴蝶优化算法的基础上采用动态开关概率,引入非线性自适应权重因子,既增加了算法前期的全局探索能力,也保证了后期的局部开发能力。同时,在迭代过程中对最优解进行逐维柯西变异,利用贪婪算法更新最优位置,引导种群向全局最优靠近,通过对4种常用的Benchmark函数的性能测试,表明改进的蝴蝶优化算法无论是在单峰函数还是多峰函数上的全局寻优能力明显优于遗传算法和粒子群算法。采用不同算法针对3种理论地质模型的频散曲线进行反演,发现改进蝴蝶优化算法在频散曲线含10%随机噪声的情况下仍然能够得到与理论模型更加接近的反演结果。最后将改进蝴蝶优化算法应用于实际瑞利波数据,反演结果与实际钻孔揭露的地层分布情况高度吻合。且与遗传算法和粒子群算法相比,改进蝴蝶优化算法在收敛速度、求解精度和稳定性方面都有显著的提升,具有一定的实用价值和应用前景。Due to the multiplicity of solutions and the multiple extrema of the inversion objection functions,conventional nonlinear optimization algorithms are susceptible to unstable convergence and local optimum in the inversion of Rayleigh wave dispersion curves.This study improved the standard butterfly optimization algorithm by incorporating dynamic switch probability and nonlinear self-adaptive weight factors,yielding an elevated global exploration capacity in the early stage and a high local research ability in the latter stage.Furthermore,the dimension-by-dimension Cauchy mutation,along with a greedy algorithm,was employed to update the current best position during each iteration,ultimately directing the whole swarm population toward the global optimum.Tests of four commonly used benchmark functions demonstrate that the improved butterfly optimization algorithm(IBOA)outperformed other nonlinear algorithms,including the genetic algorithm and particle swarm optimization algorithm,in terms of the global research capacity of both unimodal and multimodal functions.Different algorithms were adopted for the inversion of the dispersion curves of three theoretical geological models.The results show that IBOA yielded inversion results that were closer to the models even when the dispersion curves contained 10%random noise.Finally,the IBOA was applied to actual Rayleigh wave data,and the inversion results were highly consistent with the strata revealed by drilling.Compared with the genetic algorithm and the particle swarm optimization algorithm,the IBOA significantly improved the convergence speed,as well as solution accuracy and stability.Therefore,the IBOA has a certain practical value and application prospects.

关 键 词：频散曲线 改进蝴蝶优化算法 反演 非线性优化 

分 类 号：P631.4[天文地球—地质矿产勘探]