2022
First-passage probability estimation of high-dimensional nonlinear stochastic dynamic systems by a fractional moments-based mixture distribution approach
C. Ding1, C. Dang1, M. Valdebenito2, M. Faes3, M. Broggi1, M. Beer1
1 Institute for Risk and Reliability, Leibniz University Hannover, Callinstr. 34, Hannover 30167, Germany
2 Faculty of Engineering and Sciences, Universidad Adolfo Ibáñez, Av. Padre Hurtado 750, 2562340 Viña del Mar, Chile
3 Chair for Reliability Engineering, TU Dortmund University, Leonhard-Euler-Str. 5, Dortmund 44227, Germany
Journal: Mechanical Systems and Signal Processing, Volume 185, 15 February 2023, 109775
Abstract:
First-passage probability estimation of high-dimensional nonlinear stochastic dynamic systems is a significant task to be solved in many science and engineering fields, but remains still an open challenge. The present paper develops a novel approach, termed ‘fractional moments-based mixture distribution’, to address such challenge. This approach is implemented by capturing the extreme value distribution (EVD) of the system response with the concepts of fractional moment and mixture distribution. In our context, the fractional moment itself is by definition a high-dimensional integral with a complicated integrand. To efficiently compute the fractional moments, a parallel adaptive sampling scheme that allows for sample size extension is developed using the refined Latinized stratified sampling (RLSS). In this manner, both variance reduction and parallel computing are possible for evaluating the fractional moments. From the knowledge of low-order fractional moments, the EVD of interest is then expected to be reconstructed. Based on introducing an extended inverse Gaussian distribution and a log extended skew-normal distribution, one flexible mixture distribution model is proposed, where its fractional moments are derived in analytic form. By fitting a set of fractional moments, the EVD can be recovered via the proposed mixture model. Accordingly, the first-passage probabilities under different thresholds can be obtained from the recovered EVD straightforwardly. The performance of the proposed method is verified by three examples consisting of two test examples and one engineering problem.
The effect of random field parameter uncertainty on the response variability of composite structures
George Stefanoua,∗, Dimitrios Savvasa, Panagiotis Gavallasa, Iason Papaioannoub
a Institute of Structural Analysis & Dynamics of Structures, Department of Civil Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
b Engineering Risk Analysis Group, Technische Univ. München, 80290 München, Germany
Journal: Composites Part C: Open Access, Volume 9, October 2022, 100324, 109775
Abstract:
The accurate quantification of the random spatial variation of material properties at different scales is crucial
for the systematic propagation of uncertainties through engineering models. In a previous work, the spatial
variability of the apparent material properties of two-phase composites has been quantified in a Bayesian
framework. This framework enables a consistent modeling of the statistical uncertainty in the parameters of
the respective mesoscale random fields and also allows selecting the most plausible correlation model among
different models belonging to the Matérn family. In this work, the most plausible random field model is
employed in the context of uncertainty propagation of composite structures. Sample functions of the mesoscale
random fields are generated using a covariance decomposition approach and the response variability of various
composite structures is computed through Monte Carlo simulation. Parametric investigations are conducted to
highlight the effect of the identified parameter uncertainty on structural response variability.
2023
Increasing design flexibility by manually adapting the solution space for crashworthiness
P. Ascia1, V. A. Lange2, F. Duddeck1
1 TUM School of Engineering and Design, Technical University of Munich, Arcisstr. 21, 80333, Munich, Germany
2 Research and Innovation Center, BMW Group, Knorrstr. 147, 80788, Munich, Germany
Journal: Journal of Mathematics in Industry, Volume 13, article number 9, (2023)
Abstract:
The solution space methodology, as presented in 2013, was meant to guide developers at the very beginning of the development process of a new mechanically crashworthy car. Several attempts were already made to use this methodology at later development stages. However, they all encountered problems related to its very strict and demanding corridors, thus constricting the design parameters. To allow more flexibility, two different approaches were proposed to relax the initial strict conditions. The first introduced temporal dependencies to widen the corridors. The second locally changed the corridors to adapt to the needs of the development, introducing dependencies between components. We, on the contrary, propose a new method to increase flexibility without introducing any kind of dependencies. We manage this by computing the intervals of solution space under user-defined conditions, hence selecting a custom set of independent corridors that fits the data gathered during development; i.e.: force-deformation curves that can be measured during a drop-tower test simulation. This new methodology of the adaptive solution space allows designers to edit the corridors, in order to have more flexibility for fulfilling high-level requirements when independently designing new components.
Mechanical properties of graphene nanoplatelets containing random structural defects
P. Gavallas1, D. Savaas1, G. Stefanou1
1 Institute of Structural Analysis & Dynamics of Structures, Department of Civil Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
Journal: Mechanics of materials, Volume 180, May 2023, 104611
Abstract:
Graphene nanoplatelets (GNPs) consist of a small number of graphene sheets connected through van der Waals forces and, like graphene, offer exceptional mechanical, thermal and electric properties. In this work, GNPs are considered as potential reinforcements in composites and their equivalent mechanical properties are computed. Similarly to graphene, the mechanical behavior of GNPs is greatly affected by the presence of structural defects and therefore, a parametric investigation is conducted herein. Three types of planar defects are considered: Stone–Wales, single vacancy and double vacancy defects. The examined parameters include the defect type, density, distribution as well as the number of graphene layers. The Molecular Structural Mechanics approach is employed to simulate the lattice of each graphene sheet, where the C–C covalent bonds are modeled by energetically equivalent beam elements. The van der Waals interactions between two carbon atoms belonging to different graphene sheets are modeled using truss elements with mechanical properties based on Lennard-Jones potential. Equivalent properties are computed by employing a homogenization-like procedure and random fields of the stiffness tensor are obtained through the moving window technique. A severe reduction of the stiffness of GNPs is observed for vacancy defects, which also lead to considerable variability. Inplane behavior, which differs greatly from out of plane behavior, is shown to be much more susceptible to the effect of defects.
2024
Estimation of Response Expectation Bounds underParametric P-Boxes by Combining Bayesian GlobalOptimization with Unscented Transform
C. Ding1, C. Dang1, M. Broggi1, M. Beer1
1 Institute for Risk and Reliability, Leibniz University Hannover, Callinstr. 34, Hannover 30167, Germany
Journal: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, Volume 10, Issue 2, Feb 28, 2024
Abstract:
In engineering analysis, propagating parametric probability boxes (p-boxes) remains a challenge because a computationally expensive nested solution scheme is involved. To tackle this challenge, this paper proposes a novel optimization-integration method to propagate parametric probability boxes (p-boxes), mainly focusing on estimating the lower and upper bounds of structural response expectation for linear and moderately nonlinear problems. A model-based optimization scheme, named Bayesian global optimization, is first introduced to explore the space of distribution parameters. Subsequently, an efficient numerical integration method, named unscented transform, is employed to estimate the response expectation with a given set of distribution parameters. Compared with existing optimization-integration methods, the proposed method has three advantages. First, the response expectation bounds are successively estimated, allowing for the reuse of samples generated from the lower-bound estimation in the upper-bound estimation. Second, the approximation error introduced by the numerical integration method is considered. Third, computational efficiency in both the optimization and integration processes is improved. Four applications are investigated to validate the effectiveness of the proposed method, showing its ability to balance computational efficiency and accuracy when evaluating response expectation bounds.
Digital twins in safety analysis, risk assessment and emergency management
E. Zio1,2, L. Miqueles1
1 Energy Department, Politecnico di Milano, Via Privata Giuseppe La Masa 34, Milano 20156, MI, Italy
2 MINES Paris-PSL University, Centre de Recherche sur les Risques et les Crises (CRC), Sophia Antipolis, France
Journal: Reliability Engineering and System Safety , Volume 246, June 2024, 110040
Abstract:
Digital twins (DTs) represent an emerging technology that is currently leveraging the monitoring of complex systems, the implementation of autonomous control systems, and assistance during accidents and emergencies in real time. However, aspects such as safety, cybersecurity and reliability of DTs are still open issues that have not been comprehensively addressed. These aspects can offer new insights to evaluate the risk and return obtained from the implementation of DTs. This paper presents a systematic literature review of DTs focused on their use in safety analysis, risk assessment and emergency management. The aim of this work is twofold: (i) to point at the latest advancements in this technology by presenting a catalog of expected functions and twinning enabling technologies in the application domains of interest; and (ii) to point at the limitations and pending challenges on the implementation of DTs for safety analysis, risk assessment and emergency management.
