Distilling slow process probability density from fast random data

doi:10.1016/j.ymssp.2022.109156

Distilling slow process probability density from fast random data

2022-08-01

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DOI：10.1016/j.ymssp.2022.109156

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This paper addresses the following question: Starting from discrete state data collected from a randomly excited dissipative nonlinear system, is it possible to directly distill the probability density of slowly varying processes hidden in it? The answer turns out to be affirmative! This work provides a data-driven methodology to solve two successive sub-problems: extracting slow processes hidden in fast state data and identifying the probability density of slow process from the data of calculated slow process. The former resorts to a mathematical definition of slow process and an optimization algorithm, while the latter depends on the principle of maximum information entropy. The application and efficacy of this method are demonstrated by three typical nonlinear examples, i.e., two single-degree-of-freedom systems and one two-degree-of-freedom system. This method is equation-free, which circumvents stochastic differential equations and attending traditional methods. Thus, the proposed methodology is especially suitable to complex systems without derivation of associated accurate governing equations.

Keywords:

Data-driven method

Slow processes

Fast processes

Probability density

Information entropy

Distilling slow process probability density from fast random data

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