Levenberg-Marquardt法与Gauss-Newton法相结合在桥梁结构静力参数识别中的应用

目前用于服役桥梁结构静力参数识别的算法主要有Gauss-Newton(G-N)法和Levenberg-Marquardt(L-M)法,但是两种方法各有缺点,G-N法不能有效地处理奇异和非正定矩阵以及对初始点要求苛刻,L-M法虽然能克服G-N法迭代矩阵奇异的缺点,但由于阻尼因子的存在使得识别结果精度较为粗糙。结合二者的优缺点提出:先采用L-M法进行初步识别,再由L-M法初步识别结果作为G-N法的初始值进行再识别的方法,通过MATLAB自编程序实现对实际结构参数的优化求解,从而提高参数识别精度。文中最后以一连续粱的数值模拟试验验证了该法的有效性,比较结果表明,本文方法的识别精度要达到L-M法的2倍之多,能大大地提高识别结果的精度,从而保证了识别参数的可靠性,为服役桥梁结构的进一步状态评估提供了结构模型可靠的量化信息。

Application of the Combination of Levenberg-Marquart with Gauss-Newton in Static Parameter Identification of Bridge Structure

Now,the methods used to identify the service bridge structure static parameters are mostly Levenberg-Marquardt algorithm and Gauss-Newton algorithm.However,the singular iterative matrix and harsh terms of initial value can't be overcome in Gauss-Newton algorithm.While using Levenberg-Marquardt algorithm can meliorate the Gauss-Newton algorithm,the identification result from Levenberg-Marquardt algorithm is rough.Therefore,the new method has been put forward,in which the result of Levenberg-Marquardt algorithm used firstly is regarded as the initial value of Gauss-Newton algorithm.The precision of the identification will be improved by using this method.In order to validate the method,numerical simulative test on a continuous beam with three spans has been carried out.Using the method,the precision of identification is 2 times higher than that using Levenberg-Marquardt algorithm.The result indicates that using the method can guarantee the reliability of strucrue parameters.Then the quantitative and reliable message can be put forward for structural condition assessment.