超声层析成像中的一种非线性反演方法
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摘要
将模拟退火算法应用于超声层析成像,以避免对初始模型的依赖,并在全局范围内搜寻最优解。为合理确定模拟退火算法的各项参数和规则,在对超声波速进行反演时,进行如下设计:以声波走时误差的二阶范数作为目标函数;以逐渐缩小的邻域对波速向量进行随机扰动,并根据先验信息对新解进行取模约束;以Me-tropolis准则接受新解;通过实验获得合理的初始温度;以指数函数进行降温。为最大程度逼近最优解,需要跟踪保持历史最优解。经过数值模拟及对混凝土桩基的实际测算,证明了该方法的有效性。
imulated annealing algorithm is applied to ultrasonic tomography imaging to avoid dependence on initial model and search for the optimal solution in global range.To determine the rational parameters and rules of simulated annealing algorithm,the following design should be adopted while inversing ultrasonic wave speed: second-order norm of ultrasonic wave travel time error is adopted to be the objective function;wave speed vector is randomly disturbed with decreasing neighborhood;new solution is modular and constrained according to prior information,and accepted based on Metropolis rule;initial temperature is acquired rationally through experiment;annealing is performed in index function.The best solution so far is tracked and recorded for approaching the optimal solution of maximal degree.After numerical simulation and practical estimation of concrete pile foundation,the proposed method is proved to be effective.
imulated annealing algorithm is applied to ultrasonic tomography imaging to avoid dependence on initial model and search for the optimal solution in global range.To determine the rational parameters and rules of simulated annealing algorithm,the following design should be adopted while inversing ultrasonic wave speed: second-order norm of ultrasonic wave travel time error is adopted to be the objective function;wave speed vector is randomly disturbed with decreasing neighborhood;new solution is modular and constrained according to prior information,and accepted based on Metropolis rule;initial temperature is acquired rationally through experiment;annealing is performed in index function.The best solution so far is tracked and recorded for approaching the optimal solution of maximal degree.After numerical simulation and practical estimation of concrete pile foundation,the proposed method is proved to be effective.
引文
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[2]Sen M K,Stoffa P L.Nonlinear one-dimensionalseismic waveform inversion using simulated annea-ling[J].Geophysics,1991,56(10):1 624-1 638.
[3]Rothman D H.Nonlinear inversion,statistical me-chanics and residual statistics estimation[J].Geo-physics,1985,50(12):2 797-2 807.
[4]Kirkpatrick S,Gelatt C,Vecchi M.Optimizationby simulated annealing[J].Science,1983,220:671-680.
[5]Aarts E,Korst J.Simulated annealing and Boltz-mann machines[M].New York:John Wiley andSons,1989:16-39.
[6]罗亚中,唐国金,田蕾.基于模拟退火算法的最优控制问题全局化[J].南京理工大学学报,2005,29(2):144-148.
[7]靳丽霞,唐焕文,李斌.一类连续函数模拟退火算法及其收敛性分析[J].计算数学,2005,27(1):19-30.
[8]Rothman D H.Automatic estimation of large resid-ual statics corrections[J].Geophysics,1986,51(2):332-346.
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