STRUCTURAL INFLUENCE LINE IDENTIFICATION: INVERSE PROBLEM IDENTIFIABILITY ANALYSIS AND REDUCED-DIMENSION BAYESIAN UNCERTAINTY QUANTIFICATION
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摘要: 结构影响线识别是移动荷载下既有结构评估的理论基础，其本质上是基于系统输入-输出含噪数据反向对静力系统指定截面的响应函数进行识别。已有研究虽然取得了进展，但它们在以下两个方面存在局限性：缺乏反问题可识别性分析；缺乏不确定性量化。反问题可识别性分析是为了厘清系统识别的参数的解的情况。不确定性量化是基于测量输入-输出含噪数据估计影响线参数的后验概率密度函数。针对上述两个局限性，该文在贝叶斯概率框架的基础上开展关于影响线识别的反问题可识别性分析与贝叶斯不确定性量化。该文进行基于直接参数化的影响线识别，包括系统输入与输出、反问题可识别性分析、参数最优值。经分析得出：一方面，直接参数化无法保证全局模型可识别；另一方面，现有方法即使是全局模型可识别的情况下也无法进行不确定性量化。为保证反问题是全局模型可识别且同时获取参数后验概率密度函数，该文提出基于降维贝叶斯不确定性量化的影响线后验识别，包括系统输入与输出重构、反问题可识别性分析、后验概率密度函数。该文进行模拟数据下新光大桥吊杆拉力影响线识别，与实测及模拟数据下简支梁桥应变影响线识别，验证提出方法的有效性。Abstract: Structural influence line identification is the theoretical basis of evaluation for an existing structure under moving loads, which is essentially to identify the response function of a specified section of a static system based on finite dimensional input-output noisy data. Despite progress in previous researches, there are limitations in two aspects, i.e., lack of identifiability analysis of inverse problem and lack of Uncertainty Quantification (UQ). The identifiability analysis of the inverse problem is to clarify the solution situation of the parameters. UQ is to estimate the posterior probability density function (PDF) of the influence line based on the measured input-output noisy data. For these two limitations, this paper conducts the inverse problem identifiability analysis and Bayesian UQ of influence line identification based on Bayesian probability framework. This paper identifies influence lines based on direct parameterization, including system input and output, inverse problem identifiability analysis and optimal values of parameters. The results show that: direct parameterization cannot guarantee that the model is globally model-identifiable; even if the model is globally model-identifiable, the existing methods can only obtain the optimal values of the parameters. In order to ensure the globally model-identifiable case and to obtain the posterior PDF of the parameters simultaneously, the posterior identification of influence lines based on reduced-dimension Bayesian UQ is proposed, including system input and output reconstruction, inverse problem identifiability analysis and posterior PDF. The effectiveness of the proposed method is verified by identifying the influence lines of the suspender force of the Xinguang Bridge using simulated data, and the influence lines of the strain of a simply supported beam bridge using measured and simulated data.
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图 2 不同工况的识别影响线后验最优值与后验95%置信区间
Figure 2. Posterior optimal values and 95% confidence intervals of identified influence lines of different cases
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图 3 不同工况下识别影响线的残差绝对值与标准差箱线图
Figure 3. Box plots of absolute values of residuals and standard deviations of identified influence lines of different cases
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图 4 m2-Q20-d80工况下不同参数位置间隔长度的识别影响线的残差绝对值与标准差箱线图
Figure 4. Box plots of absolute values of residuals and standard deviations of identified influence lines by different interval lengths of position of parameter under the case of m2-Q20-D80
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图 5 实测数据和模拟数据下三种方法的识别影响线
Figure 5. Identified influence lines by three different methods using measured and simulated datasets
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图 6 模拟数据下三种方法的识别影响线的残差绝对值与标准差箱线图
Figure 6. Box plots of absolute values of residuals and standard deviations of identified influence lines by three different methods using simulated datasets
表 1 车辆荷载工况与降维贝叶斯方法参数工况
Table 1 Different cases of vehicle loads and parameters of reduced-dimension Bayesian uncertainty quantification
目的 车辆荷载工况 降维贝叶斯方法参数工况 车队车辆
数工况车间距
工况降维模
型种类影响线参数位置
间隔长度Δx/m检验不同车辆荷载
工况下降维贝叶斯方
法的有效性Q20 d80 m1 10 Q20 d100 m1 10 Q80 d80 m1 10 Q80 d100 m1 10 Q20 d80 m2 10 Q20 d100 m2 10 Q80 d80 m2 10 Q80 d100 m2 10 探索影响线参数位置
间隔长度对降维贝叶斯
方法识别效果的影响Q20 d80 m2 5 Q20 d80 m2 20 Q20 d80 m2 40 Q20 d80 m2 80 
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