Relaxed power spectrum estimation from multiple data records utilising subjective probabilities
Relaxed power spectrum estimation from multiple data records utilising subjective probabilities
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DOI：
10.1016/j.ymssp.2021.108346
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发表时间：
2022-02
影响因子：
8.4
通讯作者：
Marco Behrendt;M. Bittner;Liam A. Comerford;M. Beer;Jianbing Chen
中科院分区：
文献类型：
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作者：
Marco Behrendt;M. Bittner;Liam A. Comerford;M. Beer;Jianbing Chen
在结构动力学中，考虑统计不确定性是必要的，以确保载荷和材料参数的真实建模。众所周知，对于给定的输入参数，任何确定性分析仅构成单个结果。由于任意或认识的不确定性，许多因素必须考虑在一定的时间间隔或主观概率。特别是对于环境过程，如地震或风荷载，未来事件特征的可靠预测对于安全结构的设计是重要的。这项工作出席的统计过程模拟的动态系统的响应行为下的激励描述的随机过程。该过程的一个通用选项是根据真实的数据记录估计功率谱密度（PSD）函数。PSD函数确定主频率及其对随机过程的影响幅度。有许多方法用于从源数据估计PSD函数，但通常这些估计器不考虑数据记录中固有的不确定性，因为它们在数据和估计的PSD函数之间具有严格的数学关系。为了解决这个问题，随机负荷模型，捕捉认知的不确定性，包括固有的统计差异，存在于整个真实的数据集的方法提出。由于可用数据的增加，可以从相似PSD函数的集合中提取可靠的统计信息，这些相似PSD函数例如在形状和峰值频率上仅略有不同。基于这些统计数据，PSD函数模型是利用主观概率来捕捉认知的不确定性，并有效地表示这些信息。谱密度被表征为随机变量，而不是采用离散值，因此PSD函数本身表示非平稳随机过程，其包括针对给定数据集的可能有效PSD函数的范围。这种新的表示是可用于生产非遍历过程实现立即适用于蒙特卡洛模拟分析。数值算例表明了该方法的优点和优越性。
In structural dynamics, the consideration of statistical uncertainties is imperative to ensure a realistic modelling of loading and material parameters. It is well-known that any deterministic analysis only constitutes a single result for the given input parameters. Because of aleatoric or epistemic uncertainties, many factors must be considered either in certain intervals or with subjective probabilities. Especially for environmental processes, such as earthquakes or wind loads, a reliable prediction of future event characteristics is important for the design of safe structures. This work attends to the statistical procedure of simulating the response behaviour of a dynamic system under an excitation described by a stochastic process. A versatile option for this procedure is the estimation of the Power Spectral Density (PSD) function from real data records. The PSD function determines dominant frequencies and their magnitude of influence on the stochastic process. There are numerous methods for estimating the PSD function from source data, but usually these estimators do not account for uncertainties inherent in data records as they have a rigorous mathematical relationship between data and estimated PSD function. To address this issue, an approach for a stochastic load model that captures epistemic uncertainties by encompassing inherent statistical differences that exist across real data sets is proposed. Due to an increase in available data, reliable statistical information can be extracted from an ensemble of similar PSD functions that differ, for instance, only slightly in shape and peak frequency. Based on these statistics, a PSD function model is derived utilising subjective probabilities to capture the epistemic uncertainties and represent this information effectively. The spectral densities are characterised as random variables instead of employing discrete values, and thus the PSD function itself represents a non-stationary random process comprising a range of possible valid PSD functions for a given data set. This novel representation is useable for producing non-ergodic process realisations immediately applicable for Monte Carlo simulation analyses. The strengths and advantages are demonstrated by means of numerical examples.