The traditional Monte Carlo Simulation (MCS) approach can provide high reliability analysis accuracy, however, with low computational efficiency. Especially, it is computationally expensive to evaluate a very small failure probability. In this paper, a Subset Simulation-based Reliability Analysis (SSRA) approach is combined with the Multidisciplinary Design Optimization (MDO) to improve the computational efficiency in the Reliability based Multidisciplinary Design Optimization (RBMDO) problems. Furthermore, the Sequential Optimization and Reliability Assessment (SORA) approach is utilized to decouple the RBMDO into MDO and reliability analysis. The formula of MDO with SSRA within the framework of SORA (MDO-SSRA-SORA) is proposed to solve the design optimization problem of hydraulic transmission mechanism.

Fatigue damage under variable amplitude loading is related to load histories, such as load sequences and load interactions. Many nonlinear damage models have been developed to present load sequences, but load interactions are often ignored. This paper provides a new approach to present load interaction effects for nonlinear damage accumulation. It is assumed that the ratio of two consecutive stress levels is used to describe the phenomenon on damage evolution. By introducing the approach to a nonlinear fatigue model without load interactions, a modified model is developed to predict the residual fatigue life under variable amplitude loading. Experimental data from three metallic materials and welded joints in the literature are employed to verify the effectiveness of the proposed method under two-level loading. The result shows that the modified model predicts more satisfactory estimations than the primary model and Miner rule. Furthermore, the proposed method is calibrated and validated by the case of multilevel loading. It is found that the modified model shows a good estimation and its damage curve presents a typical nonlinear behavior of damage growth. It is also convenient to calculate the residual fatigue life by the Wöhler curve.

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Feature selection is an effective way of improving classification, reducing feature dimension, and speeding up computation. This work studies a reported support vector machine (SVM) based method of feature selection. Our results reveal discrepancies in both its feature ranking and feature selection schemes. Modifications are thus made on which our SVM-based method of feature selection is proposed. Using the weighting fusion technique and the one-against-all approach, our binary model has been extensively updated for multi-class classification problems. Three benchmark datasets are employed to demonstrate the performance of the proposed method. The multi-class model of the proposed method is also used for feature selection in planetary gear damage degree classification. The results of all datasets exhibit the consistently effective classification made possible by the proposed method.

Based on kernel density estimation (KDE) and Kullback-Leibler divergence (KLID), a new data-driven fault diagnosis method is proposed from a statistical perspective. The ensemble empirical mode decomposition (EEMD) together with the Hilbert transform is employed to extract 95 time-and frequency-domain features from raw and processed signals. The distance-based evaluation approach is used to select a subset of fault-sensitive features by removing the irrelevant features. By utilizing the KDE, the statistical distribution of selected features can be readily estimated without assuming any parametric family of distributions; whereas the KLID is able to quantify the discrepancy between two probability distributions of a selected feature before and after adding a testing sample. An integrated Kullback-Leibler divergence, which aggregates the KLID of all the selected features, is introduced to discriminate various fault modes/damage levels. The effectiveness of the proposed method is demonstrated via the case studies of fault diagnosis for bevel gears and rolling element bearings, respectively. The observations from the case studies show that the proposed method outperforms the support vector machine (SVM)-based and neural network-based fault diagnosis methods in terms of classification accuracy. Additionally, the influences of the number of selected features and the training sample size on the classification performance are examined by a set of comparative studies.