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Uncertainties in dynamic response of buildings with non-linear base-isolators

Design of new materials is quite a difficult task owing to various time and length scales and affiliated uncertainties. The major challenge is to include all these in a conventional model. Hyperparameter models in machine learning can be used to overcome these issues. In this paper, an artificial neural network (ANN) model is developed to estimate the effective elastic parameters of unidirectional fiber reinforced composites using representative volume elements (RVE) considering uncertainty in the fiber diameter. The diameter probability distribution is constructed from the acquired gray images by employing image processing operations. The generalized Polynomial Chaos (gPC) expansion is then used to represent the distribution as a random input parameter for finite element analysis, from where the effective parameters are realized. Similarly, the outputs of the FE model, i.e., elastic parameters, are approximated by gPC expansions having unknown deterministic coefficients and random orthogonal Hermite polynomials. A set of collocation points are generated from roots of the random polynomials; from there, the unknown coefficients are estimated. The realization samples are utilized to train an ANN algorithm based on supervised deep learning. The developed ANN model is later tested and validated for a new sample set of data. It is shown that the ANN model with few hidden layers and neurons has a high accuracy for estimation of the elastic parameters directly from the information on the distribution of fiber diameters.

This paper employs automatic differentiation (AD) in the compressive sensing-based generalized polynomial chaos (gPC) expansion, which computes a sparse approximation of the Quantity of Interest (QoI) using orthogonal polynomials as basis functions. An earlier approach without AD relies on an iterative procedure to refine the solution by approximating the gradient of the QoI. With AD, the gradient can be accurately evaluated, and a set of basis functions of the gPC expansion associated with new random variables can be efficiently identified. The computational complexity of the algorithm using AD is independent of the number of basis functions, whereas an earlier algorithm had complexity proportional to the square of this number. Our test problems include synthetic problems and a high-dimensional stochastic partial differential equation. With the new basis, the coefficient vector in the gPC expansion is sparser than the original basis. We demonstrate that introducing AD can greatly improve the performance by computing solutions 2 to 10 times faster than an earlier approach. The accuracy of the gPC expansion is also improved; sparse gpC expansions are obtained without iterative refinement, even for high dimensions when an earlier approach fails.

The electromagnetic properties of SRF cavities are mostly determined by their shape. Due to fabrication tolerances, tuning and limited resolution of measurement systems, the exact shape remains uncertain. In order to make assessments for the real life behaviour it is important to quantify how these geometrical uncertainties propagate through the mathematical system and influence certain electromagnetic properties, like the resonant frequencies of the structure’s eigenmodes. This can be done by using non-intrusive straightforwardmethodslikeMonte-Carlo(MC)simulations. However, such simulations require a large number of deterministic problem solutions to obtain a sufficient accuracy. In order to avoid this scaling behaviour, the so-called generalized polynomial chaos (gPC) expansion is used. This technique allows for the relatively fast computation of uncertainty propagation for few uncertain parameters in the case of computationally expensive deterministic models. In this paper we use the gPC expansion to quantify the propagation of uncertain geometry on the example of single cell cavities used for BESSY VSR as well as to compare the obtained results with the MC simulation.

High-dimensional uncertainty quantification for Mars atmospheric entry using adaptive generalized polynomial chaos

RF-MEMS devices area complex systems governed by the interaction of a variety of forces, including electrostatics, solid deformation, fluid damping and contact. The performance and reliability of these devices is strongly dependent on device geometry and composition, and also on material microstructure and related properties. In this paper, we consider multiscale simulation of RF MEMS switched. At the device level, we introduce a comprehensive integrated numerical framework to simulate the major governing physics and their interactions. At the micron scale, we develop a mesoscale contact model to describe the history-dependent force-displacement relationships in terms of the surface roughness, the long-range attractive interaction between the two surfaces, and the repulsive interaction between contacting asperities (including elastic and plastic deformation). The inputs to this model are obtained from atomic level simulations and nanoscale surface topography characterization. The mesoscale contact model is integrated in the device-level simulation to predict the pull-in and pull-out behavior of these switches. The uncertainties associated with the simulation are quantified and propagated using a non-intrusive collocation method based on generalized Polynomial Chaos (gPC) expansions. With such a framework, we are able to predict the PDFs of pull-in and pull-out voltage, identify the critical factors that have the most influence on the quantities of interest, and therefore guide resource allocation and risk-informed decision-making.

In the framework of process safety studies, consequence assessment of accidental scenarios is a crucial step affecting the eventual risk profile associated with the facilities under analysis. Conventional models used for consequence assessment are based on integral models, and may not be adequate to cope with the dynamic evolution of accidental scenarios and their three‐dimensional features. On the other hand, consequence assessment models based on computational fluid dynamics (CFD) approaches are promising to cope with complex scenarios and environments, but setting the simulation introduces relevant uncertainties associated with both the input data, assumptions, and with the modelling of physical effects involved. In the present study, uncertainty quantification (UQ) techniques are applied to support advanced safety studies based on CFD simulations of hazardous gas dispersion. Firstly, the accidental scenarios are characterized by defining release scenarios and conditions and quantifying source terms using integral models. At the same time, input meteorological data are gathered. This enables the development of high‐fidelity CFD simulations of gas dispersion based on different input sets and eventually the implementation of UQ techniques. The generalized polynomial chaos (gPC) expansion is employed to obtain hazardous gas concentration based on the variation of wind direction and speed. The present method is applied for the analysis of a real plant featuring a complex layout. The results show the advantages of the present approach by quantifying the influence of meteorological conditions and providing indications for supporting the development of protection systems and emergency measures.

An intrusive spectral method of probabilistic load flow (PLF) is proposed in the paper, which can handle the uncertainties arising from renewable energy integration. Generalized polynomial chaos (gPC) expansions of dependent random variables are utilized to build a spectral stochastic representation of PLF model. Instead of solving the coupled PLF model with a traditional, cumbersome method, a modified stochastic Galerkin (SG) method is proposed based on the P-Q decoupling properties of load flow in power system. By introducing two pre-calculated constant sparse Jacobian matrices, the computational burden of the SG method is significantly reduced. Two cases, IEEE 14-bus and IEEE 118-bus systems, are used to verify the computation speed and efficiency of the proposed method.

Left ventricular assist devices (LVADs) have been used for end‐stage heart failure patients as a therapeutic option. The aortic valve plays a critical role in heart failure and its treatment with a LVAD. The cardiovascular‐LVAD model is often used to investigate the physiological demands required by patients and predict the hemodynamic of the native heart supported with a LVAD. As it is a “bridge-to-recovery” treatment, it is important to maintain appropriate and active dynamics of the aortic valve and the cardiac output of the native heart, which requires that the LVAD pump be adjusted so that a proper balance between the blood contributed through the aortic valve and the pump is maintained. In this paper, we investigate how the pump power of the LVAD pump can affect the dynamic behaviors of the aortic valve for different levels of activity and different severities of heart failure. Our objective is to identify a critical value of the pump power (i.e., breakpoint) to ensure that the LVAD pump does not take over the pumping function in the cardiovascular‐pump system and share the ejected blood with the left ventricle to help the heart to recover. In addition, the hemodynamic often involves variability due to patients’ heterogeneity and the stochastic nature of the cardiovascular system. The variability poses significant challenges to understanding dynamic behaviors of the aortic valve and cardiac output. A generalized polynomial chaos (gPC) expansion is used in this work to develop a stochastic cardiovascular‐pump model for efficient uncertainty propagation, from which it is possible to rapidly calculate the variance in the aortic valve opening duration and the cardiac output in the presence of variability. The simulation results show that the gPC‐based cardiovascular‐pump model is a reliable platform that can provide useful information to understand the effect of the LVAD pump on the hemodynamic of the heart.

A Bayesian mixed shrinkage prior procedure for spatial–stochastic basis selection and evaluation of gPC expansions: Applications to elliptic SPDEs

This article addresses the problem of quantifying the uncertainty in planning aircraft ground movement operations using towbarless robotic tractors taking into account the inherent uncertainties of the problem, specifically, the uncertainties in the weight of the aircraft and in the rolling resistance of the wheels of the main landing gear. The tractor‐aircraft system is represented as a tractor‐trailer system with random parameters characterized by means of probability density functions. The quantification of the uncertainties is conducted within an optimal control framework using the formulation of a stochastic optimal control problem, which is solved through a stochastic collocation method based on generalized polynomial chaos. Specifically, the stochastic optimal control problem is converted into a set of deterministic optimal control problems, in which a reduced number of sample values of the random parameters are employed to solve particular instances of the problem. Using these sample values, it is possible to express the obtained optimal solutions as orthogonal polynomial expansions in terms of the uncertain parameters, which allows both statistical and global sensitivity analysis of the stochastic optimal solutions to be carried out in an efficient way. The objectives of this article are to understand the effects of the uncertainties in the model parameters of the tractor‐aircraft system on the solutions of the optimal control problem and to identify which uncertain parameters have more influence on the variability of these solutions. The ultimate goal is to determine the best approach for executing aircraft ground movement operations in the presence of such uncertainties.

Uncertainty quantification in a resonant nonlinear MEMS structure

Probabilistic safety margin characterization of an integrated small modular reactor using MFM and adaptive polynomial chaos

Pressure vessel components subject to high temperature and pressure are susceptible to life-limiting creep and/or creep-induced failure. Traditional continuum damage mechanics (CDM) based creep-damage model are used extensively for the prediction and design against creep in these components. Conventional creep experiments show considerable uncertainty in the creep response of materials where scatter can span decades of creep life. The objective of this paper is to introduce the probabilistic methods into a deterministic creep-damage model in order to predict experimental uncertainty. In this study, a modified Wilshire model capable of creep deformation, damage, and rupture prediction is selected. Creep deformation data for 304 stainless steel is collected from the literature consisting of quintuplicate (five) tests at 600°C with varying stress levels. It is hypothesized that the scatter in creep data is due to: test condition (temperature fluctuations and eccentric loading), initial damage (pre-existing surface and sub-surface defects), and metallurgical (local variation in microstructure) uncertainties. Probability distribution functions (pdfs) and Monte Carlo simulations are applied to introduce the uncertainties into the modified Wilshire equations. The domain of each source of uncertainty must be defined. A systematic calibration approach is followed where the material constant for each creep curve (in the quintuple) are obtained and statistical analysis is performed on the material properties to assess the random distribution associated with each uncertain material parameter. The probabilistic calibration begins with the introduction of test condition randomness (±2°C and ±3.2% MPa of nominal temperature/stress) in accordance with the ASTM standards. Cross calibration of temperature-stress variability proceeds the approximation of initial damage uncertainty which captures the remaining scatter in the data. Deterministic calibration unveils the range of variabilities associated with the material properties. The best-fitted pdfs are assigned to each uncertain parameter and subsequently, the deterministic model is converted into a probabilistic model where reliability is a tunable factor. A large number of Monte Carlo simulation are conducted to generate probabilistic creep deformation, minimum-creep-strain-rate (MCSR), and stress-rupture (SR) predictions. It is demonstrated that the probabilistic model produces quantitatively and qualitatively good fits when compared with experimental data. Future work will be directed towards the inclusion of service condition related uncertainty (power plant, turbine blade, Gen IV nuclear reactor application) into the probabilistic framework where the uncertainties are more robust.

Fuzzy Expected Value Analysis of an Industrial Grinding Process