论文标题
概率性能模式分解（PPPD）：分析框架和随机机械系统的应用
Probabilistic Performance-Pattern Decomposition (PPPD): analysis framework and applications to stochastic mechanical systems
论文作者
论文摘要
自1900年代初以来，许多研究工作一直致力于为随机机械系统开发定量解决方案。通常，当确定了有关关注量（QOI）的完整或部分概率描述时，将问题视为解决。但是，在存在复杂的系统行为的情况下，迫切需要超越概率描述。实际上，要完全了解系统，从QOI的概率结构中提取物理表征至关重要，尤其是在以数据驱动方式获得QOI解决方案时。本文以这种观点的启发，提出了一个框架，以获取有关随机系统行为的结构性特征。该框架被命名为概率性能模式分解（PPPD）。 PPPD分析旨在将复杂的响应行为分解为规定的性能状态，以在系统响应空间中的有意义的模式，并研究如何在基本随机变量的空间中触发模式。为了说明PPPD的应用，论文研究了三个数值示例：1）一个说明性的示例，其中有假设的随机过程输入和输出； 2）具有周期性和混乱行为的随机洛伦兹系统； 3）受到随机地面运动激发的简化剪切构建模型。
Since the early 1900s, numerous research efforts have been devoted to developing quantitative solutions to stochastic mechanical systems. In general, the problem is perceived as solved when a complete or partial probabilistic description on the quantity of interest (QoI) is determined. However, in the presence of complex system behavior, there is a critical need to go beyond mere probabilistic descriptions. In fact, to gain a full understanding of the system, it is crucial to extract physical characterizations from the probabilistic structure of the QoI, especially when the QoI solution is obtained in a data-driven fashion. Motivated by this perspective, the paper proposes a framework to obtain structuralized characterizations on behaviors of stochastic systems. The framework is named Probabilistic Performance-Pattern Decomposition (PPPD). PPPD analysis aims to decompose complex response behaviors, conditional to a prescribed performance state, into meaningful patterns in the space of system responses, and to investigate how the patterns are triggered in the space of basic random variables. To illustrate the application of PPPD, the paper studies three numerical examples: 1) an illustrative example with hypothetical stochastic processes input and output; 2) a stochastic Lorenz system with periodic as well as chaotic behaviors; and 3) a simplified shear-building model subjected to a stochastic ground motion excitation.
