Abstract
Reliability assessment plays a significant role in mechanical design and improvement processes. Uncertainties in structural properties as well as those in the stochatic excitations have made reliability analysis more difficult to apply. In fact, reliability evaluations involve estimations of the so-called conditional failure probability (CFP) that can be seen as a regression problem taking the structural uncertainties as input and the CFPs as output. As powerful ensemble learning methods in a machine learning (ML) domain, random forest (RF), and its variants Gradient boosting (GB), Extra-trees (ETs) always show good performance in handling non-parametric regressions. However, no systematic studies of such methods in mechanical reliability are found in the current published research. Another more complex ensemble method, i.e., Stacking (Stacked Generalization), tries to build the regression model hierarchically, resulting in a meta-learner induced from various base learners. This research aims to build a framework that integrates ensemble learning theories in mechanical reliability estimations and explore their performances on different complexities of structures. In numerical simulations, the proposed methods are tested based on different ensemble models and their performances are compared and analyzed from different perspectives. The simulation results show that, with much less analysis of structural samples, the ensemble learning methods achieve highly comparable estimations with those by direct Monte Carlo simulation (MCS).
Highlights
Reliability describes the probability that the object realizes its functions under given conditions for a specified time period [1]
The ensemble learning methods are treated as surrogate models that can be employed to fit the conditional failure probability (CFP) of the structure
For very small failure probabilities for which direct Monte Carlo simulation (MCS) is practically impossible to realize, an importance sampling technique is employed that constructs the importance sampling density function based on the basic failure events of the mechanical structure
Summary
Reliability describes the probability that the object realizes its functions under given conditions for a specified time period [1]. Considering the relative independence between the uncertainties of the structural properties and those of the excitation, the conditional failure probability can be defined and formulated as [3]. Surrogate models are developed to deal with highly nonlinear or implicit performance functions They are introduced to reduce computational burden in reliability analysis. Assume that the function between the input variables and output response takes the following form y(x) = ŷ(x) + ε, where y(x) is the unknown response function, ŷ(x) is a certain surrogate function seen as an approximation of the real function. Combined an adaptive SVM and MCS to solve nonlinear and high-dimensional problems in reliability analysis. Other surrogate models such as metamodel, ANNs, and Kriging have been proposed by other researchers [7,8,9].
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