It has been widely recognized that the inevitable uncertainties in both operational experiments and numerical analyses require efforts to be addressed appropriately within the overall area of Computational Mechanics Engineering. This endeavor includes critical tasks such as numerical model calibration, updating, verification, and validation. Nondeterministic modeling approaches enable characterization, propagation, and quantification of the inevitable uncertainties, providing model predictions over a possible range of outcomes (distributional, interval, fuzzy, etc.) rather than a unique solution with maximum fidelity to a single experiment. Such approaches applied in structural dynamics significantly promote the tendency toward high accuracy and robustness in computer-aided engineering.

However, challenges emerge from modern developments in aerospace, automobile, and marine industries, where large-scale and multiphysical systems are designed and operated with huge parameter dimensions, varying parameter sensitivity, multifarious sources of uncertainties, high computational burden, etc. The multiphysical systems, such as vibroacoustics, thermoelastics, and fluid–solid coupled systems, present more challenging domains for nondeterministic modeling because of the severe lack of knowledge in the coupling mechanism between multiple media and environments. Thus, it requires further developments of the current techniques for uncertainty treatment to enhance the capabilities of computational simulations in Computational Mechanics Engineering.

This special section on “Uncertainty Management in Complex Multiphysics Structural Dynamics” aims to provide such a venue for both academic researchers and practicing engineers working in the interdisciplinary area of uncertainty analysis and nondeterministic modeling to present the latest developments and to set the state-of-the-art. It consists of six papers which provide a representative coverage of the topics under the scope of the special section with interconnected perspectives and interdisciplinary applications.

As a representative multiphysics dynamical system, the train–bridge interaction in the high-speed rail industry is investigated by Lu, Kim, and Chang in their paper entitled “Longitudinal seismic response of train-bridge interaction system with slip in moderate earthquakes.” A full train–bridge numerical model is developed with both nonslip and stick–slip interaction modes. This study demonstrates that the slip phenomenon might occur during a moderate earthquake where the conventional nonslip hypothesis with an infinite friction coefficient is inappropriate. This work also proposes a computationally efficient approach to calculate the longitudinal seismic responses based on the linear superposition principle, which is helpful for reliability and uncertainty analysis with huge and complex train–bridge interaction systems.

The Technical Brief co-authored by Kemper and Cross proposes the “design by analysis” methodology for window design of the Pressure Vessels for Human Occupancy (PVHO). This brief reviews the ASME PVHO codes and standards, which are actually empirical documents based on years of government-sponsored testing and development. The authors consequently propose the “design by analysis” methodology based on the verification and validation (V&V) techniques to incorporate uncertainty treatment and stochastic analysis in the process of reliable design for pressured vessel components.

Ghosh, Pandita, Atkinson, et al., from GE Research, present a compendium of the GE's Bayesian Hybrid Modeling (GEBHM) approach with demonstrations of advantages of the Bayesian methodology in the industrial context. The GEBHM framework incorporates multiple features including full-Bayesian approach, parameter calibration and updating, uncertainty propagation and quantification, model validation, outcomes visualization, and parallelization computation. Within this paper, the capability of GEBHM is demonstrated in challenging engineering applications such as the structural dynamic problem, transient problem, sensitivity analysis, and Gaussian process surrogate modeling. The future enhancements to GEGHMN are also discussed including advanced Gaussian processes and multiple modeling databases.

The following companion papers focus on an increasingly significant and popular issue with far-reaching influence on Computational Mechanics Engineering, i.e., the digital twins. The first paper by Wagg, Worden, Barthorpe, et al., presents a thorough review of the state-of-the-art for digital twins in the application of engineering dynamics focusing on key aspects to synthesize an efficient digital twin and its application in industrial engineering. This paper summarizes the key processes for digital twin synthesis including system identification, data-augmented modeling, and V&V. Further discussion on open problems and challenges involved in uncertainty treatment is also presented. In its companion paper co-authored by Worden, Cross, Barthorpe, et al., a rigorous mathematical representation of digital twins is proposed based on two new concepts: mirrors and virtualizations. This work attempts to fill the gap of digital twins' research that there is currently no universal mathematics formulation of a digital twin. This mathematical representation pays more attention to the critical component of digital twins, i.e., V&V, by generating a framework for measuring the fidelity of computational models and for quantifying the confidence when using validated models outside the original context.

The paper co-authored by Kuczkowiak, Cogan, Ouisse, et al., proposes a hybrid approach for robustness analysis and model calibration based on the info-gap theory. This work develops the info-gap uncertainty model as an indicator to assess the robustness of the dynamic response of the numerical models. The analysis does not require probabilistic assumptions since the uncertainty here is modeled by an info-gap model of uncertainty. A model calibration procedure is implemented to the info-gap model using a subset of experimental data and such that the info-gap model is consistent with real test data and provides a more realistic robustness curve for decision making in the real application.

This special section consists of multiple types of papers, including review articles, a technique brief, and research papers, focusing on various-but-interconnected topics (e.g., model updating, digital twins, Bayesian modeling, verification and validation, etc.) within a wide range of applications in high-speed train, marine, aerospace, and automobile engineering. The contributions in this special section are expected to inspire awareness, discussion, and further development of critical aspects of uncertainty treatment in Computation Mechanics Engineering.

We are grateful to all the authors who contributed their valuable works and to all reviewers whose effort and time are critical for the success of this special section. We would like to express our sincere appreciation to Professor Bilal M. Ayyub, Editor-in-Chief of the ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B, and to Ms. Deena Ziadeh for the incredible support during the organization of this special section.