Stochastic functional time-series modeling for aerospace systems: regularization and bayesian methods towards robust state estimation
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Authors
Zhou, Peiyuan
Issue Date
2025-12
Type
Electronic thesis
Thesis
Thesis
Language
en_US
Keywords
Aeronautical engineering
Alternative Title
Abstract
Future intelligent aerospace structures and aerial vehicles will possess the ability to "feel," "think," and "react" instantaneously through advanced state estimation, awareness, and self-diagnostic capabilities. To achieve this, a structural health monitoring (SHM) system is crucial, providing the aircraft with vital structural insights into both damage states and environmental and operational conditions. Current developments in vibration-based stochastic SHM methods have demonstrated robust and accurate structural state estimation results on lab-scale coupons and elements. However, the extension of vibration based methods to complex structural components remains an open field of study. As such, a thorough study is needed to address the challenges of upscaling current vibration based SHM methods to complex structures: 1) modeling structural dynamics under uncertainty, 2) formulating probabilistic state estimations, 3) alleviating ill-posedness in inverse estimations, and 4) formulating statistical assessments for the performance of the methodology. Serving this purpose, this study proposes a novel vibration-based stochastic SHM method based on the Vector-dependent Functionally Pooled Stochastic Time Series (VFP-STS) model, addressing the need for a data-driven stochastic model of the structure under varying conditions. A novel regularized stochastic system identification framework is developed for the VFP-STS model, introducing sparse regularization through the Least Absolute Shrinkage and Selection Operator (LASSO) and Adaptive LASSO (ALASSO) penalties to the Weighted Least Squares (WLS) model estimation process. The Extended Regularized Information Criterion (ERIC) is introduced as a robust criterion for model structure selection. The proposed framework enables optimized functional basis selection and consistent estimation of model parameters while accounting for heteroskedasticity. Model parsimony and robustness are improved under uncertainty. As a result, ill-posedness in the inverse damage state estimation is reduced, leading to robust state estimation. Subsequently, the Cram\'er-Rao Lower Bound (CRLB) is developed and used as a statistical criterion to assess the best achievable estimator performance. The inverse estimation of structural states is formulated as an uncertainty quantification (UQ) problem, where the comprehensive distributions of structural state parameters are inferred via the Monte-Carlo Markov Chain (MCMC) algorithm with the Adaptive Metropolis (AM) method. This approach allows for the quantification of out-of-sample uncertainty, increasing the robustness of the estimator when performing online diagnosis. Additionally, multiple prior selection strategies are proposed to circumvent the effect of globally ill-posed inverse estimation by leveraging locally well-posed convex regions within the inverse problem setup. The proposed framework is evaluated thoroughly via simulated Monte-Carlo studies, which demonstrate the model selection consistency, asymptotic statistical characteristics, and modal reconstruction accuracy. Additionally, the framework is evaluated in modal vibration experiments and wind-tunnel experiments. In general, the obtained results demonstrate the improvement in accuracy and robustness by applying ALASSO regularization and Bayesian inversion to the SHM framework centered on the VFP-STS model, constituting the first step towards up-scaling the vibration-based SHM to complex structural components.
Description
December2025
School of Engineering
School of Engineering
Full Citation
Publisher
Rensselaer Polytechnic Institute, Troy, NY