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).

Training a Deep Neural Network (DNN) from scratch requires a large amount of labeled data. For a classification task where only small amount of training data is available, a common solution is to perform fine-tuning on a DNN which is pre-trained with related source data. This consecutive training process is time consuming and does not consider explicitly the relatedness between different source and target tasks. In this paper, we propose a novel method to jointly fine-tune a Deep Neural Network with source data and target data. By adding an Optimal Transport loss (OT loss) between source and target classifier predictions as a constraint on the source classifier, the proposed Joint Transfer Learning Network (JTLN) can effectively learn useful knowledge for target classification from source data. Furthermore, by using different kind of metric as cost matrix for the OT loss, JTLN can incorporate different prior knowledge about the relatedness between target categories and source categories. We carried out experiments with JTLN based on Alexnet on image classification datasets and the results verify the effectiveness of the proposed JTLN in comparison with standard consecutive fine-tuning. This Joint Transfer Learning with OT loss is general and can also be applied to other kind of Neural Networks.

This paper proposes a unified reliability analysis framework for mechanical and structural systems equipped with Tuned Mass Dampers (TMDs), encompassing single-degree-of-freedom (1-DOF), two-degrees-of-freedom (2-DOF), and ten-degrees-of-freedom (10-DOF) configurations. The methodology integrates four main components: (i) probabilistic uncertainty modeling for mass, damping, and stiffness, (ii) Latin Hypercube Sampling (LHS) to efficiently explore parameter variations, (iii) Monte Carlo simulation (MCS) for estimating failure probabilities under stochastic excitations, and (iv) machine learning models, including Random Forest (RF), Gradient Boosting (GB), Extreme Gradient Boosting (XGBoost), and Neural Networks (NNs), to predict structural responses and failure probabilities. The results demonstrate that ensemble methods, such as RF and XGBoost, provide high accuracy and can effectively identify important features. Neural Networks perform well for capturing nonlinear behavior, although careful tuning is required to prevent overfitting. The framework is further extended to a 10-DOF structure, and the simulation results confirm that machine learning-based models are highly effective for large-scale reliability analysis. These findings highlight the synergy between simulation methods and data-driven models in enhancing the reliability of TMD systems under uncertain inputs.

This paper proposes a unified reliability analysis framework for mechanical and structural systems equipped with Tuned Mass Dampers (TMDs), encompassing single-degree-of-freedom (1-DOF), two-degree-of-freedom (2-DOF), and ten-degree-of-freedom (10-DOF) configurations. The methodology combines four main components: (i) probabilistic uncertainty modeling for mass, damping, and stiffness, (ii) Latin Hypercube Sampling (LHS) to efficiently explore parameter variations, (iii) Monte Carlo Simulation (MCS) for estimating failure probabilities under stochastic excitations, and (iv) machine lSome ML models, such as Random Forest (RF), Gradient Boosting (GB), Extreme Gradient Boosting (XGBoost), and Neural Networks (NN) are used to predict structural responses and failure probabilities. The results show that ensemble methods, such as RF and XGBoost, are accurate. They can highlight important features as well. Neural Networks work well for nonlinear behavior, however, careful tuning is necessary to prevent overfitting. We also extended to a 10-DOF structure. These simulation results show that ML-based models are useful for large-scale reliability analysis. These findings also show how simulation methods and data-driven models work together to improve the reliability of TMD systems under uncertain inputs.

Tuned mass dampers (TMDs) are commonly used to reduce excessive vibrations in engineering structures. Although their vibration control performance has been widely studied, the reliability of TMD-equipped structures under stochastic excitations has not been sufficiently investigated. In practical applications, random loads and system uncertainties may significantly affect structural safety, and an efficient evaluation of failure probability remains a challenging task. Thus, the applications of these methods are greatly limited in vibration control. In this work, the structural reliability of systems equipped with TMDs is analyzed by adopting the first-passage time (FPT) as the failure criterion. Numerical investigations are performed on continuous beam models with TMDs under different types of stochastic excitation. In addition, an experimental study on a two-story steel frame structure is conducted to further examine the reliability performance of TMD-controlled systems. To reduce the computational cost associated with Monte Carlo simulation, a data-driven classification method is employed to approximate the failure domain based on a limited number of samples. The results indicate that the proposed approach enables accurate reliability estimation with a substantial reduction in computational cost, making it suitable for large-scale reliability analysis of vibration-controlled structures under stochastic excitation. The experimental results further demonstrate the applicability of the proposed reliability assessment method for practical vibration control problems.