Development of a Relaxed Stationary Power Spectrum using Imprecise Probabilities with Application to High-rise Buildings
Development of a Relaxed Stationary Power Spectrum using Imprecise Probabilities with Application to High-rise Buildings
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DOI：
10.1109/ssci44817.2019.9002899
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发表时间：
2019-12
期刊：
影响因子：
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通讯作者：
Marco Behrendt;Liam A. Comerford;M. Beer
中科院分区：
文献类型：
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作者：
Marco Behrendt;Liam A. Comerford;M. Beer
现代的方法来解决动态问题，随机振动是主导的激励，在大多数情况下是基于功率谱的概念作为核心模型的激励和响应过程的表示。这部分是由于频谱模型在频域分析中的实际适用性。此外，可以很容易地生成兼容的时域样本。这些样本可用于复杂非线性模型所代表的系统或结构的数值性能评估。谱估计方法的发展使用系综统计来产生单个或有限数量的确定性谱，从而产生可直接应用于结构分析的谱模型。然而，测量的环境过程的属性仍然丢失。为了产生可靠的和现实的功率谱的应用系统，在大多数情况下，没有足够的真实的数据集是可用的。为了通过考虑存在于真实的数据集之间的固有统计差异来捕获模型的认知不确定性，可以使用用于负载的随机表示的方法。在这项工作中，认知的不确定性的过程中的谱密度被捕获，通过使用一个区间的方法，结合随机性的过程中，导致一个不精确的概率模型。从集合的所有可用功率谱中，识别一个功率谱，所得到的松弛功率谱基于该功率谱。为了放松功率谱，实施间隔参数，从而形成所有估计的功率谱的包络边界。为了捕捉认知不确定性并有效地表达这些信息，在新开发的载荷表示中使用了不精确的概率，通过对单自由度系统和多自由度系统的响应谱的测定和分析，验证了松弛功率谱的有效性。
Modern approaches to solve dynamic problems, where random vibrations are the governing excitations, are in most cases based on the concept of the power spectrum as the core model for the representation of excitation and response processes. This is partly due to the practical applicability of spectral models for frequency domain analysis. In addition, compatible time-domain samples can easily be generated. Such samples can be used for numerical performance evaluation of systems or structures represented by complex non-linear models.The development of spectral estimation methods that use ensemble statistics to generate a single or finite number of deterministic spectra results in spectral models that can be applied directly in structural analysis. However, the properties of the measured environmental process are still lost.In order to produce reliable and realistic power spectra for the application to systems, in most cases not enough real data sets are available. To capture the epistemic uncertainties of the model by taking into account inherent statistical differences that exist across real data sets, an approach for a stochastic representation of the loads can be used. In this work, the epistemic uncertainties in the spectral density of the process are captured by using an interval approach which, in combination with the stochastic nature of the process, leads to an imprecise probability model. From all the available power spectra of the ensemble, one power spectrum is identified on which the resulting relaxed power spectrum is based. To relax the power spectrum, interval parameters are implemented, thereby forming an enveloping boundary for all estimated power spectra. In order to capture the epistemic uncertainties and to present this information effectively, imprecise probabilities are used in this newly developed load representation.The relaxed power spectrum is validated by application to a single-degree-of-freedom system and a multiple-degree-of-freedom system by determining and analysing the response spectra of the systems.