arXiv subjects

Styfen Schär

Publications and source records attributed to Styfen Schär.

6 recordsLinked to original sources

arXiv2026

Probabilistic function-on-function nonlinear autoregressive model for emulation and reliability analysis of stochastic dynamical systems

Constructing accurate and computationally efficient surrogate models (or emulators) for predicting dynamical system responses is critical in many engineering domains, yet remains challenging due to the strongly nonlinear and high-dimensional mapping from external excitations and system parameters to system responses. This work introduces a novel Function-on-Function Nonlinear AutoRegressive model with eXogenous inputs (F2NARX), which reformulates the recently proposed $\mathcal{F}$-NARX method from a function-on-function regression perspective. The proposed framework substantially improves predictive efficiency while maintaining high accuracy. By combining principal component analysis with Gaussian process regression, F2NARX further enables probabilistic predictions of dynamical responses via the unscented transform in an autoregressive manner. Such probabilistic prediction capabilities further facilitate active learning for first-passage probability evaluation. The effectiveness of the method is demonstrated through case studies of varying complexity. Results show that F2NARX outperforms state-of-the-art NARX model by orders of magnitude in efficiency while achieving higher accuracy in general. Meanwhile, the active learning approach enables accurate estimation of first-passage failure probabilities for dynamical systems using only a small number of training time histories.

math.DS↗

arXiv2026

Time-variant reliability using time-dependent surrogate models

Time-variant reliability analysis is a critical task for ensuring the safety of engineering dynamical systems subjected to stochastic excitations. However, assessing failure probability for realistic systems with Monte-Carlo simulation-based methods is often computationally intractable due to the high cost of the underlying models and the large number of simulations required. While surrogate models such as polynomial chaos expansions or Kriging are well-established for time-invariant reliability problems, their direct application to time-dependent systems remains challenging. This chapter introduces two advanced surrogate modeling frameworks designed specifically for dynamical systems: manifold-NARX (mNARX) and functional NARX (F-NARX). The mNARX approach constructs the surrogate on a reduced-order manifold of auxiliary state variables, enabling the efficient handling of high-dimensional inputs by embedding physical insight into a regression formulation. Conversely, the F-NARX framework exploits the functional nature of system trajectories, extracting principal component features from continuous time windows to mitigate issues associated with discrete lag selection and long-memory effects. We demonstrate the efficacy of these methods on two benchmark reliability problems: a stochastic quarter-car model and a hysteretic Bouc-Wen oscillator. The results highlight that, when combined with suitably biased experimental designs, both frameworks accurately capture the tail behavior of the system response, enabling precise and efficient estimation of first-passage probabilities.

stat.ME↗

arXiv2025

Surrogate modeling with functional nonlinear autoregressive models (F-NARX)

We propose a novel functional approach to surrogate modeling of dynamical systems with exogenous inputs. This approach, named Functional Nonlinear AutoRegressive with eXogenous inputs (F-NARX), approximates the system response based on temporal features of the exogenous inputs and the system response. This marks a major step away from the discrete-time-centric approach of classical NARX models, which determines the relationship between selected time steps of the input/output time series. By modeling the system in a time-feature space, F-NARX takes advantage of the temporal smoothness of the process being modeled, providing more stable predictions and reducing the dependence of model performance on the discretization of the time axis. In this work, we introduce an F-NARX implementation based on principal component analysis and polynomial regression. To further improve prediction accuracy, we also introduce a modified hybrid least angle regression approach to identify a sparse model structure and minimize the expected forecast error, rather than the one-step-ahead prediction error. We investigate the behavior and capabilities of our F-NARX implementation on two case studies: an eight-story building under wind loading and a three-story steel frame under seismic loading. Our results demonstrate that F-NARX has several favorable properties that make it well-suited to surrogate modeling applications.

stat.ME↗

arXiv2024

Comparison of Probabilistic Structural Reliability Methods for Ultimate Limit State Assessment of Wind Turbines

The probabilistic design of offshore wind turbines aims to ensure structural safety in a cost-effective way. This involves conducting structural reliability assessments for different design options and considering different structural responses. There are several structural reliability methods, and this paper will apply and compare different approaches in some simplified case studies. In particular, the well known environmental contour method will be compared to a more novel approach based on sequential sampling and Gaussian processes regression for an ultimate limit state case study. For one of the case studies, results will also be compared to results from a brute force simulation approach. Interestingly, the comparison is very different from the two case studies. In one of the cases the environmental contours method agrees well with the sequential sampling method but in the other, results vary considerably. Probably, this can be explained by the violation of some of the assumptions associated with the environmental contour approach, i.e. that the short-term variability of the response is large compared to the long-term variability of the environmental conditions. Results from this simple comparison study suggests that the sequential sampling method can be a robust and computationally effective approach for structural reliability assessment.

stat.AP↗

arXiv2023

Emulating the dynamics of complex systems using autoregressive models on manifolds (mNARX)

We propose a novel surrogate modelling approach to efficiently and accurately approximate the response of complex dynamical systems driven by time-varying exogenous excitations over extended time periods. Our approach, namely manifold nonlinear autoregressive modelling with exogenous input (mNARX), involves constructing a problem-specific exogenous input manifold that is optimal for constructing autoregressive surrogates. The manifold, which forms the core of mNARX, is constructed incrementally by incorporating the physics of the system, as well as prior expert- and domain- knowledge. Because mNARX decomposes the full problem into a series of smaller sub-problems, each with a lower complexity than the original, it scales well with the complexity of the problem, both in terms of training and evaluation costs of the final surrogate. Furthermore, mNARX synergizes well with traditional dimensionality reduction techniques, making it highly suitable for modelling dynamical systems with high-dimensional exogenous inputs, a class of problems that is typically challenging to solve. Since domain knowledge is particularly abundant in physical systems, such as those found in civil and mechanical engineering, mNARX is well suited for these applications. We demonstrate that mNARX outperforms traditional autoregressive surrogates in predicting the response of a classical coupled spring-mass system excited by a one-dimensional random excitation. Additionally, we show that mNARX is well suited for emulating very high-dimensional time- and state-dependent systems, even when affected by active controllers, by surrogating the dynamics of a realistic aero-servo-elastic onshore wind turbine simulator. In general, our results demonstrate that mNARX offers promising prospects for modelling complex dynamical systems, in terms of accuracy and efficiency.

stat.CO↗

arXiv2020

Nucleation of frictional sliding by coalescence of microslip

The onset of frictional motion is mediated by the dynamic propagation of a rupture front, analogous to a shear crack. The rupture front nucleates quasi-statically in a localized region of the frictional interface and slowly increases in size. When it reaches a critical nucleation length it becomes unstable, propagates dynamically and eventually breaks the entire interface, leading to macroscopic sliding. The nucleation process is particularly important because it determines the stress level at which the frictional interface fails, and therefore, the macroscopic friction strength. However, the mechanisms governing nucleation of frictional rupture fronts are still not well understood. Specifically, our knowledge of the nucleation process along a heterogeneous interface remains incomplete. Here, we study the nucleation of localized slip patches on linear slip-weakening interfaces with deterministic and stochastic heterogeneous friction properties. Using numerical simulations, we analyze the process leading to a slip patch of critical size for systems with varying correlation lengths of the local friction strength. Our deterministic interface model reveals that the growth of the critical nucleation patch at interfaces with small correlation lengths is non smooth due to the coalescence of neighboring slip patches. Existing analytical solutions do not account for this effect, which leads to an overestimation of global interface strength. Conversely, when the correlation length is large, the growth of the slip patch is continuous and our simulations match the analytical solution. Furthermore, nucleation by coalescence is also observed on stochastic interfaces with small correlation length...

cond-mat.soft↗