Reliability-Based Design Optimization Using Differential-Algebraic Equations

Reliability-based design optimization (RBDO) determines optimal design parameters by incorporating reliability constraints. This paper presents a RBDO approach using differential-algebraic equations (DAEs) for modeling and constraints. DAEs provide an accurate representation of dynamic engineering systems with coupled differential and algebraic equations. However, the nonlinearity and implicit nature of DAEs pose challenges for uncertainty propagation and optimization. This study proposes an efficient RBDO methodology based on stochastic collocation to quantify uncertainty in DAEs. The DAEs are transformed into an explicit ODE system to enable direct uncertainty analysis via sampling. Optimization under reliability constraints is achieved using a sequential approximate programming strategy. The approach is demonstrated through application to optimal design of a chemical reactor system. The results indicate the DAE-based RBDO framework provides an efficient way to optimize design reliability. This methodology enables reliable design optimization for complex coupled systems across energy, aerospace, chemical, and other DAE-based engineering applications. The abstract highlights the key points of using DAEs in RBDO, the proposed methods to handle uncertainty analysis and optimization for DAEs, and the advantages of a DAE-based approach. Let me know if you would like me to modify or expand the abstract further.