An Enhanced Reliability Index Method and Its Application in Reliability-Based Collaborative Design and Optimization

When designing complex mechanical equipment, uncertainties should be considered to enhance the reliability of performance. The Reliability Index Method (RIM) is a powerful tool which has been widely utilized in engineering design under uncertainties. To reduce computational cost in RIM, first or second order Taylor approximation is introduced to convert nonlinear probability constraint to the equivalent linear constraint during optimization process. Generally, this approximation process is performed at Most Probable Point (MPP) to reduce the loss of reliability analysis accuracy. However, it is difficult for the original RIM to be utilized in the situation that MPP is collinear and RIM has the same direction with the gradient of performance function at MPP. To tackle the above challenges, an Enhanced RIM (ERIM) is proposed in this study. The Collaborative Optimization (CO) strategy is combined with ERIM. The formula of CO using ERIM is given to solve reliability-based multidisciplinary design and optimization problems. A design problem of the speed reducer is utilized in this study to show the effectiveness of the proposed method.