scholarly journals The new importance measures based on vector projection for multivariate output: application on hydrological model

2016 ◽  
Author(s):  
Liyang Xu ◽  
Zhenzhou Lu ◽  
Sinan Xiao
Keyword(s):  
Polynomial Chaos ◽  
Hydrological Model ◽  
Sufficient Information ◽  
Decomposition Approach ◽  
Mathematical Properties ◽  
Sensitivity Indices ◽  
Vector Projection ◽  
Potential Benefits ◽  
Input Variables ◽  
Output Space

Abstract. Analyzing the effects of the inputs on the correlated multivariate output is important to assess risk and make decisions in Hydrological processes. However, the existing methods, such as output decomposition approach and covariance decomposition approach, cannot provide sufficient information of the effects of the inputs on the multivariate output, since these methods only measure the influence of input variables on the magnitudes of variances of the dimensionalities in the multiple output space and ignore the effects on the dimensionality directions of output variances. In this paper, a new kind of sensitivity indices based on vector projection for the multivariate output is proposed. By the projection of the conditional vectors on the unconditional vector in the dimensionless multiple output space, the new sensitivity indices measure the influence of the input variables on the magnitudes of variances and directions of the dimensionalities simultaneously. The mathematical properties of the proposed index are discussed, and its link with the Sobol indices is derived. And Polynomial Chaos Expansion (PCE) is used to estimate the proposed sensitivity indices. The results for two numerical examples and a hydrological model indicate the validity and potential benefits of the vector projection index and the efficiency of estimation approach.

scholarly journals A Global Sensitivity Analysis Framework for Hybrid Simulation

2021 ◽  
Author(s):  
Giuseppe Abbiati ◽  
Stefano Marelli ◽  
Nikolaos Tsokanas ◽  
Bruno Sudret ◽  
Bozidar Stojadinovic
Keyword(s):  
Sensitivity Analysis ◽  
Hybrid Model ◽  
Polynomial Chaos ◽  
Global Sensitivity Analysis ◽  
Hybrid Simulation ◽  
Polynomial Chaos Expansion ◽  
Chaos Expansion ◽  
Analysis Framework ◽  
Global Sensitivity ◽  
Sensitivity Indices

Hybrid Simulation is a dynamic response simulation paradigm that merges physical experiments and computational models into a hybrid model. In earthquake engineering, it is used to investigate the response of structures to earthquake excitation. In the context of response to extreme loads, the structure, its boundary conditions, damping, and the ground motion excitation itself are all subjected to large parameter variability. However, in current seismic response testing practice, Hybrid Simulation campaigns rely on a few prototype structures with fixed parameters subjected to one or two ground motions of different intensity. While this approach effectively reveals structural weaknesses, it does not reveal the sensitivity of structure's response. This thus far missing information could support the planning of further experiments as well as drive modeling choices in subsequent analysis and evaluation phases of the structural design process.This paper describes a Global Sensitivity Analysis framework for Hybrid Simulation. This framework, based on Sobol' sensitivity indices, is used to quantify the sensitivity of the response of a structure tested using the Hybrid Simulation approach due to the variability of the prototype structure and the excitation parameters. Polynomial Chaos Expansion is used to surrogate the hybrid model response. Thereafter, Sobol' sensitivity indices are obtained as a by-product of polynomial coefficients, entailing a reduced number of Hybrid Simulations compared to a crude Monte Carlo approach. An experimental verification example highlights the excellent performance of Polynomial Chaos Expansion surrogates in terms of stable estimates of Sobol' sensitivity indices in the presence of noise caused by random experimental errors.

The Nonlinear Gaussian Spectrum of Log-Normal Stochastic Processes and Variables

1999 ◽  
Vol 66 (4) ◽  
pp. 964-973 ◽  
Author(s):  
R. Ghanem
Keyword(s):  
Stochastic Processes ◽  
Polynomial Chaos ◽  
Analytical Investigation ◽  
Polynomial Chaos Expansion ◽  
Stochastic Finite Element Method ◽  
Chaos Expansion ◽  
Mathematical Properties ◽  
Log Normal ◽  
Exponential Operator ◽  
Gaussian Spectrum

A procedure is presented in this paper for developing a representation of lognormal stochastic processes via the polynomial chaos expansion. These are processes obtained by applying the exponential operator to a gaussian process. The polynomial chaos expansion results in a representation of a stochastic process in terms of multidimensional polynomials orthogonal with respect to the gaussian measure with the dimension defined through a set of independent normalized gaussian random variables. Such a representation is useful in the context of the spectral stochastic finite element method, as well as for the analytical investigation of the mathematical properties of lognormal processes.

scholarly journals Global Sensitivity Analysis of Fuzzy Distribution Parameter on Failure Probability and Its Single-Loop Estimation

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Lei Cheng ◽  
Zhenzhou Lu ◽  
Luyi Li
Keyword(s):  
Sensitivity Analysis ◽  
Failure Probability ◽  
Global Sensitivity Analysis ◽  
Computational Cost ◽  
Single Loop ◽  
Global Sensitivity ◽  
Sensitivity Indices ◽  
Distribution Parameters ◽  
Input Variables ◽  
Sampling Probability

An extending Borgonovo’s global sensitivity analysis is proposed to measure the influence of fuzzy distribution parameters on fuzzy failure probability by averaging the shift between the membership functions (MFs) of unconditional and conditional failure probability. The presented global sensitivity indices can reasonably reflect the influence of fuzzy-valued distribution parameters on the character of the failure probability, whereas solving the MFs of unconditional and conditional failure probability is time-consuming due to the involved multiple-loop sampling and optimization operators. To overcome the large computational cost, a single-loop simulation (SLS) is introduced to estimate the global sensitivity indices. By establishing a sampling probability density, only a set of samples of input variables are essential to evaluate the MFs of unconditional and conditional failure probability in the presented SLS method. Significance of the global sensitivity indices can be verified and demonstrated through several numerical and engineering examples.

scholarly journals From wind to loads: wind turbine site-specific load estimation with surrogate models trained on high-fidelity load databases

2018 ◽  
Vol 3 (2) ◽  
pp. 767-790 ◽  
Author(s):  
Nikolay Dimitrov ◽  
Mark C. Kelly ◽  
Andrea Vignaroli ◽  
Jacob Berg
Keyword(s):  
Wind Turbine ◽  
Nearest Neighbor ◽  
Polynomial Chaos ◽  
Surrogate Models ◽  
Polynomial Chaos Expansion ◽  
High Fidelity ◽  
Chaos Expansion ◽  
Site Specific ◽  
Sensitivity Indices ◽  
Fatigue Loads

Abstract. We define and demonstrate a procedure for quick assessment of site-specific lifetime fatigue loads using simplified load mapping functions (surrogate models), trained by means of a database with high-fidelity load simulations. The performance of five surrogate models is assessed by comparing site-specific lifetime fatigue load predictions at 10 sites using an aeroelastic model of the DTU 10 MW reference wind turbine. The surrogate methods are polynomial chaos expansion, quadratic response surface, universal Kriging, importance sampling, and nearest-neighbor interpolation. Practical bounds for the database and calibration are defined via nine environmental variables, and their relative effects on the fatigue loads are evaluated by means of Sobol sensitivity indices. Of the surrogate-model methods, polynomial chaos expansion provides an accurate and robust performance in prediction of the different site-specific loads. Although the Kriging approach showed slightly better accuracy, it also demanded more computational resources.

Moment Matching for Sensitivity Analysis of Probabilistic Model Output

2004 ◽  
Author(s):  
Mahmoud Awad ◽  
Agus Sudjianto ◽  
Nanua Singh
Keyword(s):  
Sensitivity Analysis ◽  
Simulation Models ◽  
Moment Matching ◽  
Model Output ◽  
Sensitivity Indices ◽  
Variance Contribution ◽  
Complex Engineering ◽  
Input Variables ◽  
The Relationship ◽  
Effective Sensitivity

With the advent of highly complex engineering simulation models that describe the relationship between input variables and output response, the need for an efficient and effective sensitivity analysis is more demanding. In this article, a generalized approach that can provide efficient as well as accurate global sensitivity indices is developed. The approach consists of two steps: running an orthogonal array based experiment using moment-matched levels of the input variables and followed by a variance contribution analysis. The benefits of the approach are demonstrated through three different examples.

scholarly journals PROBABILISTIC ANALYSIS OP SEAFLOOR LIQUEFACTION

1988 ◽  
Vol 1 (21) ◽  
pp. 101 ◽  
Author(s):  
Rafael Blazquez ◽  
Felipe M. Martinez
Keyword(s):  
Soil Layer ◽  
Water System ◽  
Deterministic Models ◽  
Risk Models ◽  
First Order ◽  
Sensitivity Indices ◽  
Reliability Method ◽  
Input Variables ◽  
Relationship Of ◽  
The Relationship

To investigate the reliability of a sandy soil layer in an ocean wave environment a liquefaction model is used in conjunction with a first order reliability method. Thus, sensitivity indices of the soil-water system with respect to the uncertain strength and input variables are computed, and the relative importance of the various factors defining the problem can be determined. The relationship of this approach with more conventional design methods (deterministic models, risk models) is discussed along with the range of applicability of the different safety measurements.

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