Related papers: Data-Driven Estimation of Failure Probabilities in…
Data-driven predictive control based on the fundamental lemma by Willems et al. is frequently considered for deterministic LTI systems subject to measurement noise. However, little has been done on data-driven stochastic control. In this…
Stochastic acceleration of charged particles due to their interactions with plasma waves may be responsible for producing superthermal particles in a variety of astrophysical systems. This process can be described as a diffusion process in…
This work presents an analysis of ocean wave data including rogue waves. A stochastic approach based on the theory of Markov processes is applied. With this analysis we achieve a characterization of the scale dependent complexity of ocean…
We demonstrate the equivalence of a Non--Markovian evolution equation with a linear memory--coupling and a Fokker--Planck equation (FPE). In case the feedback term offers a direct and permanent coupling of the current probability density to…
The simulation of stochastic wind loads is necessary for many applications in wind engineering. The proper orthogonal decomposition (POD)-based spectral representation method is a popular approach used for this purpose due to its…
The most frequently used in physical application diffusive (based on the Fokker-Planck equation) model leans upon the assumption of small jumps of a macroscopic variable for each given realization of the stochastic process. This imposes…
We propose a systematic method to derive the asymptotic behaviour of the persistence distribution, for a large class of stochastic processes described by a general Fokker-Planck equation in one dimension. Theoretical predictions are…
This paper explores the effectiveness of data-driven models to predict voltage excursion events in power systems using simple categorical labels. By treating the prediction as a categorical classification task, the workflow is characterized…
Various engineering systems such as naval and aerial vehicles, offshore structures, and mechanical components of motorized systems, are exposed to fatigue failures due to stochastic loadings. Methods for early failure prediction are…
A distribution system can flexibly adjust its substation-level power output by aggregating its local distributed energy resources (DERs). Due to DER and network constraints, characterizing the exact feasible power output region is…
Stochastic processes are encountered in many contexts, ranging from generation sizes of bacterial colonies and service times in a queueing system to displacements of Brownian particles and frequency fluctuations in an electrical power grid.…
To address the environmental concern and improve the economic efficiency, the wind power is rapidly integrated into smart grids. However, the inherent uncertainty of wind energy raises operational challenges. To ensure the cost-efficient,…
Existing studies on the degree correlation of evolving networks typically rely on differential equations and statistical analysis, resulting in only approximate solutions due to inherent randomness. To address this limitation, we propose an…
This paper proposes a joint input and state dynamic estimation scheme for power networks in microgrids and active distribution systems with unknown inputs. The conventional dynamic state estimation of power networks in the transmission…
This paper is concerned with the Fokker-Planck (FP) description of classical stochastic systems with discrete time delay. The non-Markovian character of the corresponding Langevin dynamics naturally leads to a coupled infinite hierarchy of…
We study a stochastic program where the probability distribution of the uncertain problem parameters is unknown and only indirectly observed via finitely many correlated samples generated by an unknown Markov chain with $d$ states. We…
We consider a nonlinear stochastic differential equation driven by an $\alpha$-stable L\'{e}vy process ($1<\alpha<2$). We first obtain some regularity results for the probability density of its invariant measure via establishing the a…
Addressing the uncertainty introduced by increasing renewable integration is crucial for secure power system operation, yet capturing it while preserving the full nonlinear physics of the grid remains a significant challenge. This paper…
The simulation of complex stochastic network dynamics arising, for instance, from models of coupled biomolecular processes remains computationally challenging. Often, the necessity to scan a models' dynamics over a large parameter space…
We present a data-driven approach to efficiently approximate nonlinear transient dynamics in solid-state systems. Our proposed machine-learning model combines a dimensionality reduction stage with a nonlinear vector autoregression scheme.…