The results are as follows : based on the nonlinear least square optimization technique and singular value decomposition method , the back - analysis method for estimating material properties is established 以非线性最小二乘的优化原理为基础，并结合奇异值分解，开发了基于非线性最小二乘的路面模量反演算法。
The sirt inversion operator can be applied to solve the large - scale sparse linear equation and velocity tomographic inversion can be performed based on direct arrival traveltime and accuracy could be 3 meters 研究成功的sirt反演算法可用于求解大型稀疏超定线性方程组，根据直达波旅行时进行速度层析反演，其精度可达到3米。
In the calculating example of model inversion , the proper sampling interval and ' trend - band ' method were selected and inversion errors of the linear density and axes depth of cylinder were close to 0 . 25 % and 3 . 8 % , respectively 在模型反演算例中，选择了适当的采样间隔和“趋势镶边”法，反演的圆柱体线密度和轴心深度误差分别为0 . 25 %和3 . 8 % 。
Since 1994 , the algorithms retrieving the vertical structure of precipitation have occurred , gprof algorithm is one of them , which developed by kummerow and olson and used by nasa to retrieve precipitation using tmi data operationally 自1994年以来又发展了多种降水垂直结构反演算法，其中kummerow 、 olson等人发展的gprof算法较为成熟，是美国nasa用以处理tmi资料的业务降水反演算法。
The random error analysis of the method gives the relative deviation of 8 % - 10 % ) for the method of deriving co . it shows that the column content of co and other atmospheric minor gases can be well derived using this method , and the retrieval algorithm is very simple and effective 原理和数据分析表明，该测量方法可以较好地反演出大气co等微量气体的柱总量。对co大气柱总量的反演精度可达到8 - 10 。反演算法简单易用。
With analogizing the evolution process of atomic transition from excited states to ground state , we proposed a novel non - linear optimization algorithm for geophysical inverse problem , called as simulated atomic transition algorithm ( sata ) 在此基础上，模拟了物理学中原子从激发态向基态跃迁的物理过程，建立了一种与原子跃迁过程相对应的非线性随机跃迁数学模型和模型解跃迁搜索准则，导出了适用于一般地球物理资料的模拟原子跃迁的非线性反演算法。
Considering the nonuniqueness and instability of ultrasonic computerized tomography for structural concrete as well as the ultrasonic transmission characteristics in concrete , a natural weight matrix with dear physical meaning was introduced in the inverse algorithm 摘要针对混凝土超声波层析成像结果不唯一和稳定性差的问题，首先依据超声波在混凝土中的传播特点，在反演算法中引入物理意义明确的自然权矩阵，对走时较小的射线和射线较密的成像单元加以重权。
It is shown that only the inversion incorporating topography , in which the topography is directly incorporated into the inversion algorithm , can effectively erase the topographic influence and correct the error in inversion result , obtaining the inverted model in agreement with subsurface geoelectrical structure 结果表明，只有将地形直接带入反演算法中，进行带地形电阻率三维反演才能有效消除地形影响及其对反演结果的偏差，得到与地下电性结构相符的反演结果。
Through the comparison among three methods , the back - analysis method based on the nonlinear least square optimization technique , the back - analysis method based on the genetic algorithm and modulus program , their advantages and disadvantages are studied . the data from the actual pavement is analyzed by the method based on the nonlinear least square optimization technique 将基于非线性最小二乘的路面模量的反演算法、基于遗传算法的路面模量反演算法以及国际上知名度较高的路面模量反分析软件modulus软件这三个反算程序进行了比较，并分析了它们各自的优缺点，找到了它们各自的适用范围，从而为它们的协同工作奠定了基础。
It introduced research actual state of genetic algorithms , enumerated the calculation result of global optimized crossover and mutation , gave the mostly program of binary system character string coding and using numerical model and the practical data checked out the effectiveness of mixed inversion algorithm 文中介绍了遗传算法的研究现状，例举了全局寻优交叉和变异的计算结果，给出了二进制字符串编码的主要程序段，用数值模型与实际资料验正了混合反演算法的有效性。
