Reliability-based design optimization using kriging surrogates and subset simulation

The aim of the present paper is to develop a strategy for solving reliability-based design optimization (RBDO) problems that remains applicable when the performance models are expensive to evaluate. Starting with the premise that simulation-based approaches are not affordable for such problems, and that the most-probable-failure-point-based approaches do not permit to quantify the error on the estimation of the failure probability, an approach based on both metamodels and advanced simulation techniques is explored. The kriging metamodeling technique is chosen in order to surrogate the performance functions because it allows one to genuinely quantify the surrogate error. The surrogate error onto the limit-state surfaces is propagated to the failure probabilities estimates in order to provide an empirical error measure. This error is then sequentially reduced by means of a population-based adaptive refinement technique until the kriging surrogates are accurate enough for reliability analysis. This original refinement strategy makes it possible to add several observations in the design of experiments at the same time. Reliability and reliability sensitivity analyses are performed by means of the subset simulation technique for the sake of numerical efficiency. The adaptive surrogate-based strategy for reliability estimation is finally involved into a classical gradient-based optimization algorithm in order to solve the RBDO problem. The kriging surrogates are built in a so-called augmented reliability space thus making them reusable from one nested RBDO iteration to the other. The strategy is compared to other approaches available in the literature on three academic examples in the field of structural mechanics.Comment: 20 pages, 6 figures, 5 tables. Preprint submitted to Springer-Verla

Reliability-based design optimization of shells with uncertain geometry using adaptive Kriging metamodels

Optimal design under uncertainty has gained much attention in the past ten years due to the ever increasing need for manufacturers to build robust systems at the lowest cost. Reliability-based design optimization (RBDO) allows the analyst to minimize some cost function while ensuring some minimal performances cast as admissible failure probabilities for a set of performance functions. In order to address real-world engineering problems in which the performance is assessed through computational models (e.g., finite element models in structural mechanics) metamodeling techniques have been developed in the past decade. This paper introduces adaptive Kriging surrogate models to solve the RBDO problem. The latter is cast in an augmented space that "sums up" the range of the design space and the aleatory uncertainty in the design parameters and the environmental conditions. The surrogate model is used (i) for evaluating robust estimates of the failure probabilities (and for enhancing the computational experimental design by adaptive sampling) in order to achieve the requested accuracy and (ii) for applying a gradient-based optimization algorithm to get optimal values of the design parameters. The approach is applied to the optimal design of ring-stiffened cylindrical shells used in submarine engineering under uncertain geometric imperfections. For this application the performance of the structure is related to buckling which is addressed here by means of a finite element solution based on the asymptotic numerical method

An adaptive sampling method for global sensitivity analysis based on least-squares support vector regression

In the field of engineering, surrogate models are commonly used for approximating the behavior of a physical phenomenon in order to reduce the computational costs. Generally, a surrogate model is created based on a set of training data, where a typical method for the statistical design is the Latin hypercube sampling (LHS). Even though a space filling distribution of the training data is reached, the sampling process takes no information on the underlying behavior of the physical phenomenon into account and new data cannot be sampled in the same distribution if the approximation quality is not sufficient. Therefore, in this study we present a novel adaptive sampling method based on a specific surrogate model, the least-squares support vector regresson. The adaptive sampling method generates training data based on the uncertainty in local prognosis capabilities of the surrogate model - areas of higher uncertainty require more sample data. The approach offers a cost efficient calculation due to the properties of the least-squares support vector regression. The opportunities of the adaptive sampling method are proven in comparison with the LHS on different analytical examples. Furthermore, the adaptive sampling method is applied to the calculation of global sensitivity values according to Sobol, where it shows faster convergence than the LHS method. With the applications in this paper it is shown that the presented adaptive sampling method improves the estimation of global sensitivity values, hence reducing the overall computational costs visibly

Quantile-based optimization under uncertainties using adaptive Kriging surrogate models

Uncertainties are inherent to real-world systems. Taking them into account is crucial in industrial design problems and this might be achieved through reliability-based design optimization (RBDO) techniques. In this paper, we propose a quantile-based approach to solve RBDO problems. We first transform the safety constraints usually formulated as admissible probabilities of failure into constraints on quantiles of the performance criteria. In this formulation, the quantile level controls the degree of conservatism of the design. Starting with the premise that industrial applications often involve high-fidelity and time-consuming computational models, the proposed approach makes use of Kriging surrogate models (a.k.a. Gaussian process modeling). Thanks to the Kriging variance (a measure of the local accuracy of the surrogate), we derive a procedure with two stages of enrichment of the design of computer experiments (DoE) used to construct the surrogate model. The first stage globally reduces the Kriging epistemic uncertainty and adds points in the vicinity of the limit-state surfaces describing the system performance to be attained. The second stage locally checks, and if necessary, improves the accuracy of the quantiles estimated along the optimization iterations. Applications to three analytical examples and to the optimal design of a car body subsystem (minimal mass under mechanical safety constraints) show the accuracy and the remarkable efficiency brought by the proposed procedure

Block of voltage-gated calcium channels by peptide toxins

International audienceVenoms from various predatory species, such as fish hunting molluscs scorpions, snakes and arachnids contain a large spectrum of toxins that include blockers of voltage-gated calcium channels. These peptide blockers act by two principal manners-physical occlusion of the pore and prevention of activation gating. Many of the calcium channel-blocking peptides have evolved to tightly occupy their binding pocket on the principal pore forming subunit of the channel, often rendering block poorly reversible. Moreover, several of the best characterized blocking peptides have developed a high degree of channel subtype selectivity. Here we give an overview of different types of calcium channel-blocking toxins, their mechanism of action, channel subtype specificity, and potential use as therapeutic agents

Optimisation sous contrainte de fiabilité d une coque imparfaite

National audienceSee http://hal.archives-ouvertes.fr/docs/00/59/27/95/ANNEX/r_S5P52J4K.pd

Reliability assessment by adaptive kernel-based surrogate models - Approximation of non-smooth limit-state functions

Adaptive surrogate models are of practical use for reliability analysis based on costly-to-evaluate limit-state functions. The quality of the approximation made depends on both the selected type of surrogate model (and its related assumptions) and the adaptive scheme applied for the construction of the approximate model. Most of surrogate models assume some degree of smoothness, which allows them to be learned with a not so large set of input-output data pairs. This paper investigates the use of Matérn kernels in the context of support vector regression, with tuned regularity parameters. This kernel is used in an adaptive scheme based on MCMC sampling, whose objective is to progressively sample the failure domain. The proposed approach is applied to both a smooth and a non smooth limit-state functions, showing the benefits of using such a highly flexible kernel

Dynamic effective mass of granular media

We develop the concept of frequency dependent effective mass, M(omega), of jammed granular materials which occupy a rigid cavity to a filling fraction of 48%, the remaining volume being air of normal room condition or controlled humidity. The dominant features of M(omega) provide signatures of the dissipation of acoustic modes, elasticity and aging effects in the granular medium. We perform humidity controlled experiments and interpret the data in terms of a continuum model and a "trap" model of thermally activated capillary bridges at the contact points. The results suggest that attenuation in the granular materials is influenced significantly by the kinetics of capillary condensation between the asperities at the contacts.Comment: 4 pages, 3 figure

Regulation by protein kinase-C of putative P-type Ca channels expressed in Xenopus oocytes from cerebellar mRNA

AbstractXenopus oocytes injected with rat cerebellar mRNA expressed functional voltage-dependent Ca channels detected as an inward Ba current (IBa). The pharmacological resistance to dihydropyridines and ω-conotoxin together with the blockade obtained with Agelenopsis aperta venom suggest that these channels could be somehow assimilated to P-type Ca channels. The precise nature of the transplanted Ca channels was assessed by hybrid-arrest experiments using a specific oligonucleotide antisense-derivated from the recently cloned α1-subunit of P channels (BI-1 clone). In addition, we demonstrate that exogenous Ca channel activity was enhanced by two different PKC activators (a phorbol ester and a structural analog to diacylglycerol). The general electrophysiological and pharmacological properties of the stimulated Ca channels remain unchanged. This potentiation induced by PKC activators is antagonized by a PKC inhibitor (staurosporine) and by a monoclonal antibody directed against PKC. It is concluded that P-type Ca channels are potentially regulated by PKC phosphorylation and the functional relevance of this intracellular pathway is discussed