Metamodel-based importance sampling for structural reliability analysis

Structural reliability methods aim at computing the probability of failure of systems with respect to some prescribed performance functions. In modern engineering such functions usually resort to running an expensive-to-evaluate computational model (e.g. a finite element model). In this respect simulation methods, which may require $10^{3-6}$ runs cannot be used directly. Surrogate models such as quadratic response surfaces, polynomial chaos expansions or kriging (which are built from a limited number of runs of the original model) are then introduced as a substitute of the original model to cope with the computational cost. In practice it is almost impossible to quantify the error made by this substitution though. In this paper we propose to use a kriging surrogate of the performance function as a means to build a quasi-optimal importance sampling density. The probability of failure is eventually obtained as the product of an augmented probability computed by substituting the meta-model for the original performance function and a correction term which ensures that there is no bias in the estimation even if the meta-model is not fully accurate. The approach is applied to analytical and finite element reliability problems and proves efficient up to 100 random variables.Comment: 20 pages, 7 figures, 2 tables. Preprint submitted to Probabilistic Engineering Mechanic

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

Reliability assessment of cutting tool life based on surrogate approximation methods

A novel reliability estimation approach to the cutting tools based on advanced approximation methods is proposed. Methods such as the stochastic response surface and surrogate modeling are tested, starting from a few sample points obtained through fundamental experiments and extending them to models able to estimate the tool wear as a function of the key process parameters. Subsequently, different reliability analysis methods are employed such as Monte Carlo simulations and first- and second-order reliability methods. In the present study, these reliability analysis methods are assessed for estimating the reliability of cutting tools. The results show that the proposed method is an efficient method for assessing the reliability of the cutting tool based on the minimum number of experimental results. Experimental verification for the case of high-speed turning confirms the findings of the present study for cutting tools under flank wear

A subset multicanonical Monte Carlo method for simulating rare failure events

Estimating failure probabilities of engineering systems is an important problem in many engineering fields. In this work we consider such problems where the failure probability is extremely small (e.g $\leq10^{-10}$). In this case, standard Monte Carlo methods are not feasible due to the extraordinarily large number of samples required. To address these problems, we propose an algorithm that combines the main ideas of two very powerful failure probability estimation approaches: the subset simulation (SS) and the multicanonical Monte Carlo (MMC) methods. Unlike the standard MMC which samples in the entire domain of the input parameter in each iteration, the proposed subset MMC algorithm adaptively performs MMC simulations in a subset of the state space and thus improves the sampling efficiency. With numerical examples we demonstrate that the proposed method is significantly more efficient than both of the SS and the MMC methods. Moreover, the proposed algorithm can reconstruct the complete distribution function of the parameter of interest and thus can provide more information than just the failure probabilities of the systems

Efficient time-dependent system reliability analysis

Engineering systems are usually subjected to time-variant loads and operate under time-dependent uncertainty; system performances are therefore time-dependent. Accurate and efficient estimate of system reliability is crucial for decision makings on system design, lifetime cost estimate, maintenance strategy, etc. Although significant progresses have been made in time-independent reliability analysis for components and systems, time-dependent system reliability methodologies are still limited. This dissertation is motivated by the need of accurate and effective reliability prediction for engineering systems under time-dependent uncertainty. Based on the classic First and Second Order Reliability Method (FORM and SORM), a system reliability method is developed for multidisciplinary systems involving stationary stochastic processes. A dependent Kriging method is also developed for general components. This method accounts for dependent responses from surrogate models and is therefore more accurate than existing Kriging Monte Carlo simulation methods that neglect the dependence between responses. The extension of the dependent Kriging method to systems is also a contribution of this dissertation. To overcome the difficulty of obtaining extreme value distributions and get rid of global optimization with a double-loop procedure, a Kriging surrogate modeling method is also proposed. This method provides a new perspective of surrogate modeling for time-dependent systems and is applicable to general systems having random variables, time, and stochastic processes. The proposed methods are evaluated through a wide range of engineering systems, including a compound cylinders system, a liquid hydrogen fuel tank, function generator mechanisms, slider-crank mechanisms, and a Daniels system --Abstract, page iv

Learning for predictions: Real-time reliability assessment of aerospace systems

Prognostics and Health Management (PHM) aim to predict the Remaining Useful Life (RUL) of a system and to allow a timely planning of replacement of components, limiting the need for corrective maintenance and the down time of equipment. A major challenge in system prognostics is the availability of accurate physics based representations of the grow rate of faults. Additionally, the analysis of data acquired during flight operations is traditionally time consuming and expensive. This work proposes a computational method to overcome these limitations through the dynamic adaptation of the state-space model of fault propagation to on-board observations of system’s health. Our approach aims at enabling real-time assessment of systems health and reliability through fast predictions of the Remaining Useful Life that account for uncertainty. The strategy combines physics-based knowledge of the system damage propagation rate, machine learning and real-time measurements of the health status to obtain an accurate estimate of the RUL of aerospace systems. The RUL prediction algorithm relies on a dynamical estimator filter, which allows to deal with nonlinear systems affected by uncertainties with unknown distribution. The proposed method integrates a dynamical model of the fault propagation, accounting for the current and past measured health conditions, the past time history of the operating conditions (such as input command, load, temperature, etc.), and the expected future operating conditions. The model leverages the knowledge collected through the record of past fault measurements, and dynamically adapts the prediction of the damage propagation by learning from the observed time history. The original method is demonstrated for the RUL prediction of an electromechanical actuator for aircraft flight controls. We observe that the strategy allows to refine rapid predictions of the RUL in fractions of seconds by progressively learning from on-board acquisitions