A combined sensitivity analysis and kriging surrogate modeling for early validation of health indicators

Abstract

is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. b s t r a c tTo increase the dependability of complex systems, one solution is to assess their state of health continuously through the monitoring of variables sensitive to potential degradation modes. When computed in an operating environment, these variables, known as health indicators, are subject to many uncertainties. Hence, the stochastic nature of health assessment combined with the lack of data in design stages makes it difficult to evaluate the efficiency of a health indicator before the system enters into service. This paper introduces a method for early validation of health indicators during the design stages of a system development process. This method uses physics-based modeling and uncertainties propagation to create simulated stochastic data. However, because of the large number of parameters defining the model and its computation duration, the necessary runtime for uncertainties propagation is prohibitive. Thus, kriging is used to obtain low computation time estimations of the model outputs. Moreover, sensitivity analysis techniques are performed upstream to determine the hierarchization of the model parameters and to reduce the dimension of the input space. The validation is based on three types of numerical key performance indicators corresponding to the detection, identification and prognostic processes. After having introduced and formalized the framework of uncertain systems modeling and the different performance metrics, the issues of sensitivity analysis and surrogate modeling are addressed. The method is subsequently applied to the validation of a set of health indicators for the monitoring of an aircraft engine's pumping unit.

Variance-based global sensitivity analysis for multiple scenarios and models with implementation using sparse grid collocation

“…Another kind of widely used methods is meta-modeling to build cheap-to-compute surrogates or emulators of computationally expensive models so that performing a large number of model executions is computationally affordable (O"Hagan, 2004). The methods of developing surrogates include Taylor series approximation (Hakami et al, 2003), response surface approximation (Helton and Davis, 2003), Fourier series (Saltelli, et al, 1999) nonparametric regression (Helton, 1993;Storlie et al, 2009), Kriging (Borgonovo et al, 2012;Lamoureux et al, 2014), Gauss process (Rasmussen and Williams, 2006), polynomial chaos expansion (Garcia-Cabrejo and Valocchi, 2014;Oladyshkin et al, 2012;Sudret, 2007), and sparse-grid collocation (Buzzard, 2012;Buzzard and Xiu, 2012). However, the meta-modeling methods may still need a relatively large number of model executions to develop accurate surrogates, and the surrogate development is not always straightforward due to model nonlinearity (Razavi et al, 2012;.…”

High-resolution computational modeling of immune responses in the gut

“…The term \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$M( w )$\end{document} represents a stationary GP with mean = 0, and covariance between any points was modeled as the Gaussian covariance defined in [44]. Thus, the covariance between any design points \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}${w_a} = {( {{X_a}^T,\ {t_a}} )^T}\ $\end{document}and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}${w_b} = {( {{X_b}^T,\ {t_b}} )^T}\ $\end{document} in the random field can be modeled as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{} \begin{eqnarray*} \mathrm{cov}\left( {M\left( {{w_a}} \right),\ M\left( {{w_b}} \right)} \right) = {{\rm{\Gamma }}^2}{\rm{\ exp}}\left( - \mathop \sum \nolimits_{r\ = \ 1}^d {\theta _r}{\left( {{X_{ar}} - \ {X_{br}}} \right)^2}\right)R\left( {{t_a} - \ {t_b};{\rm{\gamma }}} \right),\nonumber \\ \end{eqnarray*} \end{document}…”

Sensitivity analysis of complex engineering systems: Approaches study and their application to vehicle restraint system crash simulation

“…Both MA and Sobol' indices could be used in SA of black-boxes systems where no specific assumption is made. Lamoureux [26] realized the SA of an aircraft engine's pumping unit by combining MA and Sobol' indices. Ge [27] discussed the sequential SA with MA and Sobol' indices of the test functions (G function, G * function, K function, M orris function): his study shows that the sequential SA has a very high accuracy in both qualitative and quantitative SA of a high-dimensional model.…”