A hybrid probabilistic framework for model validation with application to structural dynamics modeling
A hybrid probabilistic framework for model validation with application to structural dynamics modeling
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DOI：
10.1016/j.ymssp.2018.10.014
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发表时间：
2019-04
影响因子：
8.4
通讯作者：
Subhayan De;P. Brewick;Erik A. Johnson;S. Wojtkiewicz
中科院分区：
文献类型：
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作者：
Subhayan De;P. Brewick;Erik A. Johnson;S. Wojtkiewicz
识别物理系统的有用数学模型是计算建模和仿真的重要组成部分。一旦适当的模型被确定，它们可以被用于应用程序，如响应预测，结构控制，监测结构完整性，寿命预测等的模型和模型类的数量可供建模，以代表一个物理现象，但是，可以是非常大的。在整个研究过程中保留所有可用的模型可能是计算上的负担，因此建模者具有识别要在进一步研究中使用的有效模型的重大问题。为了解决这一挑战，本文提出了一个概率框架，用于通过交织模型证伪和贝叶斯模型选择的概念来验证模型。模型证伪基于测量只能用于证伪模型的理念，在该框架中用于预处理和后处理步骤，分别消除无法解释测量的模型和模型类。这是第一个研究提出了一个框架，以整合这两种范式。作者之前引入的似然约束模型伪造，使用错误发现率（FDR）确定初始候选模型类的有效性，并删除大多数不正确的模型，而不会产生任何显着的额外计算负担。接下来，将基于贝叶斯定理分配后验模型类概率的贝叶斯模型选择应用于剩余的模型类，以识别提供概率上最佳拟合数据的预测的模型和模型类。最后，一个后处理似然界证伪检查最终模型类的有效性。建议的框架首先说明通过两个非线性结构动力学的例子，表明所提出的框架在确定这些结构的模型，以及减少计算负担相对于单独应用贝叶斯模型选择的功效。最后，第三个例子使用的测量数据进行的实验，在一个全尺寸的四层楼基础隔震建筑在世界上最大的振动台在日本的“E-Defense”实验室。
Identifying useful mathematical models of physical systems is an essential part of computational modeling and simulation. Once appropriate models are identified, they can be used for applications such as response prediction, structural control, monitoring structural integrity, lifetime prognosis, etc. The number of models and model classes available to the modeler to represent a physical phenomenon, however, can be very large. Retaining all available models throughout a study can be computationally burdensome, so the modeler has the significant problem of identifying the valid models to be used in further studies. To address this challenge, a probabilistic framework is proposed herein for validating models by intertwining the concepts of model falsification and Bayesian model selection. Model falsification, based on the philosophy that measurements can only be used to falsify models, is used in this framework in both pre- and postprocessing steps to eliminate models and model classes, respectively, that cannot explain the measurements. This is the first study to propose a framework to integrate these two paradigms. A likelihood-bound model falsification, previously introduced by the authors, determines the validity of the initial candidate model classes, using the false discovery rate (FDR), and removes most of the incorrect ones without incurring any significant additional computational burden. Next, Bayesian model selection, which assigns posterior model class probabilities based on Bayes’ theorem, is applied to the remaining model classes to identify the model(s) and model class(es) that provide predictions that probabilistically best fit the data. Finally, a postprocessing likelihood-bound falsification checks the validity of the final model class(es). The proposed framework is first illustrated through two nonlinear structural dynamics examples that show the efficacy of the proposed framework in identifying models for these structures as well as reducing the computational burden relative to Bayesian model selection applied alone. Finally, a third example uses measurement data from experiments performed on a full-scale four-story base-isolated building at the world’s largest shake table in Japan’s “E-Defense” laboratory.