This study presents an efficient method for system reliability and response prognostics based on Bayesian analysis and analytical approximations. Uncertainties are explicitly included using probabilistic modeling. Usage and health monitoring information is used to perform the Bayesian updating. To improve the computational efficiency, an analytical computation procedure is proposed and formulated to avoid time-consuming simulations in classical methods. Two realistic problems are presented for demonstrations. One is a composite beam reliability analysis, and the other is the structural frame dynamic property estimation with sensor measurement data. The overall efficiency and accuracy of the proposed method is compared with the traditional simulation-based method.
TopIntroduction
Diagnostics and prognostics of modern engineering systems have drawn extensive attentions in the past decade due to their increasing complexities (Brauer & Brauer, 2009; Melchers, 1999). In particular, time-dependent reliability estimate for high reliability demanding systems such as aircraft and nuclear facilities must be quantified in order to prevent system failures. The central idea of reliability analysis involves computation of a multi-dimensional integral over the failure domain of the performance function (Ditlevsen & Madsen, 1996; Madsen, Krenk, & Lind, 1986; Rackwitz, 2001). For problems with high-dimensional parameters, the exact evaluation of this integral is either analytically intractable or computationally prohibitive (Yuen, 2010). Analytical approximations and numerical simulations are two major computational methods to solve such problems.
The simulation-based method includes direct Monte Carlo (MC) (Kalos & Whitlock, 2008), Importance Sampling (IS) (Gelman & Meng, 1998; Liu, 1996), and other MC simulations with different sampling techniques. Analytical approximation methods, such as first- and second- order reliability methods (FORM/SORM) have been developed to estimate the reliability without large numbers of MC simulations. FORM and SORM computations are based on linear (first-order) and quadratic (second-order) approximations of the limit state surface at the most probable point (MPP) in the standard normal space (Ditlevsen & Madsen, 1996; Madsen, Krenk, & Lind, 1986; Rackwitz, 2001). Under the condition that the limit state surface at the MPP is close to its linear or quadratic approximation and that no multiple MPPs exist on the limit state surface, FORM/SORM are sufficiently accurate for engineering purposes (Bucher & Bourgund, 1990; Cai & Elishakoff, 1994; Zhao & Ono, 1999). If the final objective is to calculate the system response given a reliability index, the inverse reliability method can be used. The most well-known approach is inverse FORM method proposed in (Der Kiureghian & Dakessian, 1998; Der Kiureghian, Zhang, & Li, 1994; Li & Foschi, 1998). Du, Sudjianto, and Chen (2004) proposed an inverse reliability strategy and applied it to the integrated robust and reliability design of a vehicle combustion engine piston. Saranyasoontorn and Manuel (2004) developed an inverse reliability procedure for wind turbine components. Lee, Choi, Du, and Gorsich (2008) used the inverse reliability analysis for reliability-based design optimization of nonlinear multi-dimensional systems. Cheng, Zhang, Cai, and Xiao (2007) presented an artificial neural network based inverse FORM method for solving problems with complex and implicit performance functions.