Reliability estimation of a multi-component mechanical system "speed reducer" using optimization methods

Abstract

The reliability assessment of multi-component mechanical systems, such as speed reducers, poses considerable challenges due to the numerous random variables involved and the presence of correlated failure modes. The use of Dimensionality Reduction Methods (DRMs) in structural reliability analysis provides a valuable approach to simplify these complex systems. However, their application raises important concerns related to maintaining accuracy, ensuring interpretability, and achieving computational efficiency. This thesis evaluates the limitations and applicability of Dimensionality Reduction Methods (DRMs) in solving real-world structural reliability problems. The primary objective is to develop strategies that mitigate inherent drawbacks of DRMs, such as significant information loss, challenges in interpreting principal components and their physical significance relative to the original variables, and high computational complexity. The research is structured in three stages. First, a Structural System Reliability-Based Dimension Reduction Method (SSR-DRM) is proposed, which leverages the First-Order Reliability Method (FORM) to create reduced-dimensional models based on sensitivity factors and the correlation between failure modes. Reliability is then assessed for the original, reduced-dimensional, and deterministic models to identify which simplified models most accurately represent the original system. Failure probabilities are estimated using FORM and Monte Carlo Simulation (MCS) as benchmark methods. The results consistently show that the reduced- dimensional model provides the most precise approximation of the original system across all subsystems of the speed reducer, effectively capturing essential reliability characteristics while significantly reducing computational effort. In the second stage, the reduced-dimension models from the previous phase are employed to estimate the overall reliability of the speed reducer, modeled as a series system of its components. First, the first-order failure probability bounds (i.e., the widest upper and lower bounds) are computed for the reduced models. Subsequently, the failure probability is evaluated using Ditlevsen’s second-order upper bound method (narrow bounds), incorporating sensitivity factors and the correlation matrix. The results show strong agreement with Monte Carlo Simulation (MCS) outcomes, demonstrating the efficacy of the proposed approach.