Finite element (FE) model updating in multi-objective framework helps for better understanding of overall performance in updating (under various variations of weightages assigned to basic components of the objective function) along with providing scope for better judgmental selection. A FE model updating in multi-objective framework is proposed with no requirement of repeated eigen-solution along with avoiding repeated possibilities of incurring mode-pairing error (by adopting an existing framework of system mode shape). Two multi-objective optimization techniques are adopted: (a) weighted sum and (b) adaptive weighted sum methods. Moreover, a possible single best solution out of the Pareto front is identified based on minimum modal distance value and compared with Gibbs sampling technique (without mode-matching). Two examples with multiple damage cases utilized in validating the proposed approach are as follows: (a) simulated example (ASCE benchmark structure) and (b) experimental example (four storied shear frame laboratory structure). It is observed that the proposed multi-objective framework has performed well in FE model updating in case of both simulated and experimental cases. Additionally, a connection (directly relating the multi-objective weights and error variances) is established between the proposed updating methodology and an existing Bayesian updating methodology to facilitate the probabilistic damage detection in Bayesian framework. Moreover, selection of an appropriate solution (out of the Pareto front) having suitable values of multi-objective weights facilitates to estimate the suitable values of error variances (based on the proposed connection), consequently enabling an efficient Bayesian FE model updating without requirement of any assumption of error variances.

中文翻译：

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使用不完全模态测量更新有限元模型的多目标框架

多目标框架中的有限元 (FE) 模型更新有助于更好地理解更新的整体性能（在分配给目标函数基本组件的权重的各种变化下），并为更好的判断选择提供空间。提出了一种多目标框架下的有限元模型更新，不需要重复特征解，同时避免了重复出现模式配对错误的可能性（通过采用现有的系统模式形状框架）。采用了两种多目标优化技术：(a) 加权求和和 (b) 自适应加权求和方法。此外，基于最小模态距离值确定了帕累托前沿中可能的单个最佳解决方案，并与吉布斯采样技术（无模式匹配）进行了比较。用于验证所提出方法的具有多个损坏案例的两个示例如下：（a）模拟示例（ASCE 基准结构）和（b）实验示例（四层剪切框架实验室结构）。观察到，在模拟和实验情况下，所提出的多目标框架在有限元模型更新中表现良好。此外，在提议的更新方法和现有的贝叶斯更新方法之间建立了联系（直接关联多目标权重和误差方差），以促进贝叶斯框架中的概率损坏检测。而且，