| 动载荷识别的非迭代法研究 |
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| 引用本文： | 余波,吴月,聂川宝,高强. 动载荷识别的非迭代法研究[J]. 应用数学和力学, 2019, 40(5): 473-489. DOI: 10.21656/1000-0887.390211 |
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| 作者姓名： | 余波 吴月 聂川宝 高强 |
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| 作者单位： | 1合肥工业大学 土木与水利工程学院, 合肥 230009;2大连理工大学 工业装备结构分析国家重点实验室, 辽宁 大连 116024 |
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| 基金项目： | 国家自然科学基金(11872166;11502063)；安徽省自然科学基金(1608085QA07) |
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| 摘 要： | 为了快速准确地识别结构在复杂环境下的承载状态,基于有限元法和Newmark-β法提出了一种非迭代反演方法,并用于识别结构上施加的动载荷.通过探寻测量信息与待演参量之间的关系,建立误差函数,根据最小二乘法实现动载荷的直接识别无需迭代,其中对待反演的分布载荷实施基函数展开,以提高算法的抗不适定性.同时奇异值分解法被用来求解病态方程组.数值算例分别讨论了测量噪声、测点数量、基函数展开、测点位置和不同时间步长对反演结果的影响,结果显示该方法在识别动载荷时具有较高的精度和效率.
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| 关 键 词： | 动载荷识别 非迭代反演方法 最小二乘法 基函数展开 |
| 收稿时间： | 2018-08-01 |
A Non-Iterative Method for Dynamic Load Identification |
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| YU Bo,WU Yue,NIE Chuanbao,GAO Qiang. A Non-Iterative Method for Dynamic Load Identification[J]. Applied Mathematics and Mechanics, 2019, 40(5): 473-489. DOI: 10.21656/1000-0887.390211 |
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| Authors: | YU Bo WU Yue NIE Chuanbao GAO Qiang |
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| Affiliation: | YU Bo,WU Yue,NIE Chuanbao,GAO Qiang |
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| Abstract: | To identify the load states of structures under complex environment quickly and accurately, a non iterative inversion method was proposed based on the finite element method and the Newmark-β method, and used to identify dynamic loads on structures. The relationship between the measurement information and the parameters to be identified was found out, and the error function was established. With the least squares method, the proposed method can estimate the dynamic load directly without iteration. What’s more, the basis function expansion was applied to inverse the distributed loads and help overcome the ill posedness of the algorithm. Meanwhile, the singular value decomposition method was used to solve ill conditioned equations. The effects of the measurement noise, the number of measurement points, the basis function expansion, the locations of measurement points and the time step on the inversed results were discussed in numerical examples. The results show that, the proposed method has high accuracy and efficiency for dynamic load identification problems. |
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| Keywords: | dynamic load identification non-iterative inversion method least squares method basis function expansion |
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