scholarly journals Adaptive Surrogate Modeling for Time-Dependent Multidisciplinary Reliability Analysis

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Zhen Hu ◽  
Sankaran Mahadevan
Keyword(s):  
Reliability Analysis ◽  
Uncertainty Propagation ◽  
Transient Behavior ◽  
Surrogate Models ◽  
Computational Effort ◽  
Time Step ◽  
Multidisciplinary Analysis ◽  
Coupling Variables ◽  
The Individual ◽  
Computational Resources

Multidisciplinary systems with transient behavior under time-varying inputs and coupling variables pose significant computational challenges in reliability analysis. Surrogate models of individual disciplinary analyses could be used to mitigate the computational effort; however, the accuracy of the surrogate models is of concern, since the errors introduced by the surrogate models accumulate at each time-step of the simulation. This paper develops a framework for adaptive surrogate-based multidisciplinary analysis (MDA) of reliability over time (A-SMART). The proposed framework consists of three modules, namely, initialization, uncertainty propagation, and three-level global sensitivity analysis (GSA). The first two modules check the quality of the surrogate models and determine when and where we should refine the surrogate models from the reliability analysis perspective. Approaches are proposed to estimate the potential error of the failure probability estimate and to determine the locations of new training points. The three-level GSA method identifies the individual surrogate model for refinement. The combination of the three modules facilitates adaptive and efficient allocation of computational resources, and enables high accuracy in the reliability analysis result. The proposed framework is illustrated with two numerical examples.

Adaptive Surrogate Modeling for Multidisciplinary Reliability Analysis Under Time-Dependent Uncertainty

2017 ◽  
Author(s):  
Zhen Hu ◽  
Sankaran Mahadevan
Keyword(s):  
Reliability Analysis ◽  
System Reliability ◽  
Uncertainty Propagation ◽  
Surrogate Modeling ◽  
Surrogate Models ◽  
Time Dependent ◽  
System Reliability Analysis ◽  
Training Point ◽  
Coupling Variables ◽  
Multidisciplinary System

Multidisciplinary systems will remain in transient states when time-dependent interactions are present among the coupling variables. This brings significant challenges to time-dependent multidisciplinary system reliability analysis. This paper develops an adaptive surrogate modeling approach (ASMA) for multidisciplinary system reliability analysis under time-dependent uncertainty. The proposed framework consists of three modules, namely initialization, uncertainty propagation, and three-level global sensitivity analysis (GSA). The first two modules check the quality of the surrogate models and determine when and where we should refine the surrogate models. Approaches are then proposed to estimate the potential error of the failure probability estimate and determine the location of the new training point. In the third module (i.e. three-level GSA), a method is developed to decide which surrogate model to refine, through GSA at three different levels. These three modules are integrated together systematically and enable us to adaptively allocate the computational resources to refine different surrogate models in the system and thus achieve high accuracy and efficiency in time-dependent multidisciplinary system reliability analysis. Results of two numerical examples demonstrate the effectiveness of the proposed framework.

scholarly journals Modified Dimension Reduction-Based Polynomial Chaos Expansion for Nonstandard Uncertainty Propagation and Its Application in Reliability Analysis

Processes ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1856
Author(s):  
Jeongeun Son ◽  
Yuncheng Du
Keyword(s):  
Dimension Reduction ◽  
Reliability Analysis ◽  
Structural Reliability ◽  
Polynomial Chaos ◽  
Uncertainty Propagation ◽  
Surrogate Models ◽  
Polynomial Chaos Expansion ◽  
Chaos Expansion ◽  
Computationally Efficient ◽  
Standard Distribution

This paper presents an algorithm for efficient uncertainty quantification (UQ) in the presence of many uncertainties that follow a nonstandard distribution (e.g., lognormal). Using the polynomial chaos expansion (PCE), the algorithm builds surrogate models of uncertainty as functions of a standard distribution (e.g., Gaussian variables). The key to build these surrogate models is to calculate PCE coefficients of model outputs, which is computationally challenging, especially when dealing with models defined by complex functions (e.g., nonpolynomial terms) under many uncertainties. To address this issue, an algorithm that integrates the PCE with the generalized dimension reduction method (gDRM) is utilized to convert the high-dimensional integrals, required to calculate the PCE coefficients of model predictions, into several lower-dimensional ones that can be rapidly solved with quadrature rules. The accuracy of the algorithm is validated with four examples in structural reliability analysis and compared to other existing techniques, such as Monte Carlo simulations and the least angle regression-based PCE. Our results show our algorithm provides accurate UQ results and is computationally efficient when dealing with many uncertainties, thus laying the foundation to address UQ in complex control systems.

Structural Reliability Analysis Using Adaptive Artificial Neural Networks

2019 ◽  
Vol 5 (4) ◽  
Author(s):  
Wellison José de Santana Gomes
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Reliability Analysis ◽  
Structural Reliability ◽  
Limit State ◽  
Surrogate Models ◽  
Primary Objective ◽  
Computational Effort ◽  
State Function ◽  
Artificial Neural

Abstract Structural reliability theory has been applied to many engineering problems in the last decades, with the primary objective of quantifying the safety of such structures. Although in some cases approximated methods may be used, many times the only alternatives are those involving more demanding approaches, such as Monte Carlo simulation (MCS). In this context, surrogate models have been widely employed as an attempt to keep the computational effort acceptable. In this paper, an adaptive approach for reliability analysis using surrogate models, proposed in the literature in the context of Kriging and polynomial chaos expansions (PCEs), is adapted for the case of multilayer perceptron (MLP) artificial neural networks (ANNs). The methodology is employed in the solution of three benchmark reliability problems and compared to MCS and other methods from the literature. In all cases, the ANNs led to results very close to those obtained by MCS and required much less limit state function evaluations. Also, the performance of the ANNs was found comparable, in terms of accuracy and efficiency, to the performance of the other methods.

scholarly journals Deep Neural Network and Polynomial Chaos Expansion-Based Surrogate Models for Sensitivity and Uncertainty Propagation: An Application to a Rockfill Dam

Water ◽  
2021 ◽  
Vol 13 (13) ◽  
pp. 1830
Author(s):  
Gullnaz Shahzadi ◽  
Azzeddine Soulaïmani
Keyword(s):  
Polynomial Chaos ◽  
Complex Structure ◽  
Uncertainty Propagation ◽  
Surrogate Models ◽  
Polynomial Chaos Expansion ◽  
Soil Parameters ◽  
Chaos Expansion ◽  
Rockfill Dam ◽  
Parametric Studies ◽  
The Impact

Computational modeling plays a significant role in the design of rockfill dams. Various constitutive soil parameters are used to design such models, which often involve high uncertainties due to the complex structure of rockfill dams comprising various zones of different soil parameters. This study performs an uncertainty analysis and a global sensitivity analysis to assess the effect of constitutive soil parameters on the behavior of a rockfill dam. A Finite Element code (Plaxis) is utilized for the structure analysis. A database of the computed displacements at inclinometers installed in the dam is generated and compared to in situ measurements. Surrogate models are significant tools for approximating the relationship between input soil parameters and displacements and thereby reducing the computational costs of parametric studies. Polynomial chaos expansion and deep neural networks are used to build surrogate models to compute the Sobol indices required to identify the impact of soil parameters on dam behavior.

scholarly journals Statistical Uncertainty of DNS in Geometries without Homogeneous Directions

2021 ◽  
Vol 11 (4) ◽  
pp. 1399
Author(s):  
Jure Oder ◽  
Cédric Flageul ◽  
Iztok Tiselj
Keyword(s):  
Channel Flow ◽  
A Priori ◽  
Time Integration ◽  
Navier Stokes ◽  
Statistical Uncertainty ◽  
Time Step ◽  
Order Of Magnitude ◽  
Averaging Time ◽  
The Individual ◽  
Time Required

In this paper, we present uncertainties of statistical quantities of direct numerical simulations (DNS) with small numerical errors. The uncertainties are analysed for channel flow and a flow separation case in a confined backward facing step (BFS) geometry. The infinite channel flow case has two homogeneous directions and this is usually exploited to speed-up the convergence of the results. As we show, such a procedure reduces statistical uncertainties of the results by up to an order of magnitude. This effect is strongest in the near wall regions. In the case of flow over a confined BFS, there are no such directions and thus very long integration times are required. The individual statistical quantities converge with the square root of time integration so, in order to improve the uncertainty by a factor of two, the simulation has to be prolonged by a factor of four. We provide an estimator that can be used to evaluate a priori the DNS relative statistical uncertainties from results obtained with a Reynolds Averaged Navier Stokes simulation. In the DNS, the estimator can be used to predict the averaging time and with it the simulation time required to achieve a certain relative statistical uncertainty of results. For accurate evaluation of averages and their uncertainties, it is not required to use every time step of the DNS. We observe that statistical uncertainty of the results is uninfluenced by reducing the number of samples to the point where the period between two consecutive samples measured in Courant–Friedrichss–Levy (CFL) condition units is below one. Nevertheless, crossing this limit, the estimates of uncertainties start to exhibit significant growth.

A Numerically Efficient Method for Analysis of Very Large Articulated Floating Structures

1998 ◽  
Vol 42 (03) ◽  
pp. 174-186
Author(s):  
C. J. Garrison
Keyword(s):  
Hydrodynamic Interaction ◽  
Near Field ◽  
Three Dimensional ◽  
Computational Effort ◽  
Floating Structure ◽  
Complete Structure ◽  
Field Interaction ◽  
Floating Structures ◽  
Computing Effort ◽  
The Individual

A method is presented for evaluation of the motion of long structures composed of interconnected barges, or modules, of arbitrary shape. Such structures are being proposed in the construction of offshore airports or other large offshore floating structures. It is known that the evaluation of the motion of jointed or otherwise interconnected modules which make up a long floating structure may be evaluated by three dimensional radiation/diffraction analysis. However, the computing effort increases rapidly as the complexity of the geometric shape of the individual modules and the total number of modules increases. This paper describes an approximate method which drastically reduces the computational effort without major effects on accuracy. The method relies on accounting for hydrodynamic interaction effects between only adjacent modules within the structure rather than between all of the modules since the near-field interaction is by far the more important. This approximation reduces the computational effort to that of solving the two-module problem regardless of the total number of modules in the complete structure.

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