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Abstract Model uncertainty quantification is essential for enhancing the validity of simulations of nonlinear dynamic systems. However, its effectiveness may be significantly affected when experimental or monitoring data are sparse. To tackle this challenge, we drew inspiration from population-based structural health monitoring, which enhances damage diagnostics by facilitating information sharing across a population of similar (in some context) but different systems. In this article, we propose a novel population-based model bias correction (PMBC) framework that employs federated learning (FL) to enable distributed, privacy-preserving bias correction for populations of nonlinear dynamic systems sharing a common design framework but with different system models in reality due to uncertainty in unit-specific model parameters and model-structural errors. The model uncertainty in a population of nonlinear dynamic systems is first analyzed using the Kennedy and O’Hagan (KOH) framework. The proposed method then constructs a shared nonlinear autoregressive with eXogenous inputs (NARX) surrogate model for the simulation model and develops system-specific bias datasets that capture both model-structural errors and parameter uncertainty. Federated training is employed to collaboratively learn a global bias correction model, which is subsequently fine-tuned into system-specific bias models using local datasets to correct biases in a population of nonlinear dynamic systems. The effectiveness of the proposed framework is demonstrated through two case studies, namely a population of Duffing oscillators and a fleet of three ship-heading models. In both cases, the PMBC approach is compared with a conventional single-system bias correction method, a centralized approach with and without fine-tuning, and the original simulation model. The results indicate that the proposed PMBC method consistently produces the lowest prediction errors, maintaining robust generalization under untested new input excitations. 

We present a reliability-based topology optimization method for structural assemblies represented by geometric primitives with uncertain dimensions and position using the geometry projection method. Compared with the density-based and level-set representations widely used in topology optimization, the primitive-based representation reduces the number of random variables, making the computational expense of incorporating geometric uncertainties via surrogate models practical. Moreover, the random variables are directly related to the dimensions and positions of the primitives, which is a natural description of dimensional and positional variability for assemblies made of stock material. The proposed method adopts a decoupled quantile-based scheme, whereby at each outer iteration, a deterministic topology optimization with a constraint on the limit-state function is solved; a surrogate of the limit-state function at this design is subsequently built via the univariate dimension reduction method to estimate the quantile corresponding to the target reliability, which in turn is used to update the constraint limit for the next outer iteration. The proposed approach is demonstrated through several examples and the results are compared with those of a single-loop formulation based on the first-order reliability method, showing closer satisfaction of the prescribed performance reliability targets at practical computational cost. 

Structural Health Monitoring (SHM) systems play a critical role in maintaining the safety and operational efficiency of infrastructure such as miter gates managed by the United States Army Corps of Engineers (USACE). These gates, integral to navigation and flood control systems, demand robust and efficient monitoring techniques to predict failures and thus optimize maintenance schedules. Any unexpected shutdown costs nearly three million dollars per day to the US economy. The existing traditional data centralized machine learning approaches for SHM often face challenges, including data privacy concerns, high communication costs, and computational limitations. This study mainly explores the application of Federated Learning (FL) techniques to SHM systems using three finite element miter gate models for the loss-of-contact damage detection problem. This approach addresses these challenges by enabling decentralized training of machine learning models across multiple assets. FL ensures data privacy by keeping sensitive information local while leveraging shared global models through aggregation methods. Our results demonstrate that FL can achieve comparable prediction accuracy to centralized methods while maintaining data privacy and reducing communication overhead. This framework improves model accuracy by incorporating diverse data distributions from different gates and their operational conditions. The study also highlights the scalability of FL in handling large-scale SHM systems, making it a viable solution for USACE to extend the lifespan of their critical assets. 

Abstract Bayesian inference based on computational simulations plays a crucial role in model-informed damage diagnostics and the design of reliable engineering systems, such as the miter gates studied in this article. While Bayesian inference for damage diagnostics has shown success in some applications, the current method relies on monitoring data from solely the asset of interest and may be affected by imperfections in the computational simulation model. To address these limitations, this article introduces a novel approach called Bayesian inference-based damage diagnostics enhanced through domain translation (BiEDT). The proposed BiEDT framework incorporates historical damage inspection and monitoring data from similar yet different miter gates, aiming to provide alternative data-driven methods for damage diagnostics. The proposed framework first translates observations from different miter gates into a unified analysis domain using two domain translation techniques, namely, cycle-consistent generative adversarial network (CycleGAN) and domain-adversarial neural network (DANN). Following the domain translation, a conditional invertible neural network (cINN) is employed to estimate the damage state, with uncertainty quantified in a Bayesian manner. Additionally, a Bayesian model averaging and selection method is developed to integrate the posterior distributions from different methods and select the best model for decision-making. A practical miter gate structural system is employed to demonstrate the efficacy of the BiEDT framework. Results indicate that the alternative damage diagnostics approaches based on domain translation can effectively enhance the performance of Bayesian inference-based damage diagnostics using computational simulations. 

Diagnosing lithium-ion battery health and predicting future degradation is essential for driving design improvements in the laboratory and ensuring safe and reliable operation over a product’s expected lifetime. However, accurate battery health diagnostics and prognostics is challenging due to the unavoidable influence of cell-to-cell manufacturing variability and time-varying operating circumstances experienced in the field. Machine learning approaches informed by simulation, experiment, and field data show enormous promise to predict the evolution of battery health with use; however, until recently, the research community has focused on deterministic modeling methods, largely ignoring the cell-to-cell performance and aging variability inherent to all batteries. To truly make informed decisions regarding battery design in the lab or control strategies for the field, it is critical to characterize the uncertainty in a model’s predictions. After providing an overview of lithium-ion battery degradation, this paper reviews the current state-of-the-art probabilistic machine learning models for health diagnostics and prognostics. Details of the various methods, their advantages, and limitations are discussed in detail with a primary focus on probabilistic machine learning and uncertainty quantification. Last, future trends and opportunities for research and development are discussed. 

Miter gates are vital civil infrastructure components in inland waterway transportation networks. To provide risk-informed insights for decisions related to repair and maintenance, sensors have been installed on some miter gates for monitoring. Despite the monitoring system's ability in collecting a large volume of monitoring data, accurately diagnosing damage state in such large structures remains challenging due to the lack of labeled monitoring data, since these structures are designed with high reliability and for a long operation life. This paper addresses this challenge by proposing a damage diagnostics approach for miter gates based on domain adaptation. The proposed approach consists of two main modules. In the first module, Cycle-Consistent generative adversarial network (CycleGAN) is employed to map monitoring data of a miter gate of interest and other similar yet different miter gates into the same analysis domain. Subsequently, a normalizing flow-based likelihood-free inference model is constructed within this common domain using data from source miter gates whose damage states are labeled from historical inspections. The trained normalizing flow model is then used to predict the damage state of the target miter gate based on the translated monitoring data. A case study is presented to demonstrate the effectiveness of the proposed method. The results indicate that the proposed method in general can accurately estimate the damage state of the target miter gate in the presence of uncertainty.