Technology Category
Reasoning under Uncertainty: Stochastic OptimizationSearch and Optimization: Non-convex OptimizationIntelligent Robots: State Estimation
A Wide-Sense Stationarity Test Based on the Geometric Structure of Covariance
🤖 AI Summary
This paper addresses the challenge of reliably testing wide-sense stationarity (WSS) in stochastic dynamical systems. We propose a hypothesis-free, time-varying test grounded in the geometric structure of the covariance function. Specifically, the covariance function is treated as a two-dimensional surface; a local block-wise estimator reconstructs this covariance surface, and directional derivatives along the (1,1,0) direction are computed and tested for zero to detect time-varying nonstationarity. This approach introduces differential-geometric concepts—particularly directional derivatives—to WSS testing for the first time, requiring no prior stationarity assumptions and enabling localized, time-resolved, data-driven nonstationarity identification. Numerical experiments on a single-degree-of-freedom linear system and a stochastic Duffing oscillator demonstrate the method’s robustness and sensitivity, accurately capturing evolving non-WSS behavior. The framework exhibits clear engineering applicability for real-world nonstationary signal analysis.
Technology Category
Application Category
📝 Abstract
This paper presents a test for wide-sense stationarity (WSS) based on the geometry of the covariance function. We estimate local patches of the covariance surface and then check whether the directional derivative in the $(1,1,0)$ direction is zero on each patch. The method only requires the covariance function to be locally smooth and does not assume stationarity in advance. It can be applied to general stochastic dynamical systems and provides a time-resolved view. We apply the test method to an SDOF system and to a stochastic Duffing oscillator. These examples show that the method is numerically stable and can detect departures from WSS in practice.
Problem
Research questions and friction points this paper is trying to address.
Tests wide-sense stationarity using covariance geometry
Checks directional derivative zero for local covariance patches
Applies to stochastic systems without prior stationarity assumption
Innovation
Methods, ideas, or system contributions that make the work stand out.
Test based on covariance geometry
Checks directional derivative on local patches
Requires only local smoothness, no prior stationarity
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