| 桥梁结构有限元模型的仿射-区间不确定修正 |
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| 引用本文： | 单德山,顾晓宇,李中辉,李乔.桥梁结构有限元模型的仿射-区间不确定修正[J].中国公路学报,2019,32(2):67-76. |
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| 作者姓名： | 单德山 顾晓宇 李中辉 李乔 |
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| 作者单位： | 西南交通大学土木工程学院, 四川成都 610031 |
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| 基金项目： | 国家重点基础研究发展计划项目（2013CB036300-2）；国家重点研发计划项目（2016YFC0802202）；国家自然科学基金项目（51678489）；四川省科技计划项目（2016JY0130） |
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| 摘 要： | 为获得桥梁结构的基准状态，考虑测试和结构参数的不确定性，将区间分析、仿射算法引入响应面有限元模型修正方法中，建立了一种新的桥梁结构有限元不确定模型修正方法。在讨论结构特点及力学行为的基础上，选择了待修正结构参数和结构响应后，采用均匀试验设计方法获得试验样本，同时结合多样本的有限元分析，采用F检验法得到结构响应的显著性参数。基于有限元模型修正的响应面方法，构建结构的响应面替代模型后，引入区间分析算法的自然拓展，将响应面模型拓展为区间响应面函数，同时采用仿射算法解决区间分析的区间扩张问题，构建桥梁结构有限元模型的仿射-区间不确定修正方法，并采用遗传算法进行区间优化求解。另外，针对区间响应面有限元模型修正的具体需求，提出了区间响应面函数的两步验证方法。用斜拉桥振动台模型桥梁在不同工况下的测试模态参数和斜拉索索力，对其进行有限元模型的不确定修正，实现了实测响应与有限元计算响应间误差的最小化。区间响应面函数的两步验证证实了参数修正范围和结构响应的有效性和正确性，修正后结构纵向、横向、竖向的一阶，二阶频率以及索力的实测响应均在计算响应范围内。验证结果表明：所提有限元不确定模型修正方法，能有效实现桥梁结构有限元模型的修正。
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| 关 键 词： | 桥梁工程 有限元模型修正 区间分析 斜拉桥 仿射算法 试验验证 |
| 收稿时间： | 2018-02-03 |
Affine-interval Uncertainty Updating of Finite Element Model for Cable-stayed Bridge |
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| SHAN De-shan,GU Xiao-yu,LI Zhong-hui,LI Qiao.Affine-interval Uncertainty Updating of Finite Element Model for Cable-stayed Bridge[J].China Journal of Highway and Transport,2019,32(2):67-76. |
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| Authors: | SHAN De-shan GU Xiao-yu LI Zhong-hui LI Qiao |
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| Affiliation: | School of Civil Engineering, Southwest Jiaotong University, Chengdu 610031, Sichuan, China |
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| Abstract: | Interval analysis and affine arithmetic were introduced into the updating process of the structural finite element model to address uncertainties of the measurement and structural parameters, and a novel uncertainty updating method of finite element model for bridge structure was carried out to obtain the baseline of the bridge structure based on the response surface method. Once the candidate structural parameters for updating and interesting structural responses were determined in light of the structural characteristics and their mechanical behaviors, the sample-sets for structural parameters were generated using uniform test design. Then, each set of generated structural parameters was applied as the input to the finite element model to evaluate the corresponding structural responses, and the significance of the parameters for interesting structural responses were found using F-test. The surrogate models for structural responses were achieved within the response surface framework for finite element model updating, and the natural extension method was then adopted to transform the obtained surrogate models to their corresponding models, called interval response surface functions. Moreover, affine arithmetic was incorporated into the updating process to control the inevitable interval overestimation problem of interval analysis, genetic algorithm was applied to optimize the updating interval, and affine-interval uncertainty updating method of the finite element model for bridge structure was performed. Furthermore, a two-step verification method was proposed to meet the specific requirements for the interval response surface based finite element model uncertainty updating. The modal parameters and cable tensions measured from a carefully instrumented model of a cable-stayed bridge tested on a shaking table under various testing cases were utilized to update their finite element model uncertainties, and the discrepancies between the measured and calculated structural responses for the model bridge were then minimized. It is shown from the two-step verification of the interval-response surface function that the rationality and feasibility for of updated structural parameters and their corresponding structural responses are guaranteed, and all the first and second longitudinal, lateral, and vertical measured frequencies as well as measured cable-tensions fall within the variation ranges of their corresponding calculated responses. It is thus demonstrated that the proposed uncertainty updating method for the finite element model is effective and feasible for updating the finite element models of real-world bridge structures. |
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| Keywords: | bridge engineering finite element model updating interval analysis cable-stayed bridge affine arithmetic experimental validation |
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