Abstract: To evaluate the instability probability of deep submergence ring stiffened pressure cylindrical shell structures with small failure probability， an innovative adaptive analysis method based on Gaussian process classification (GPC) and importance sampling (IS) was proposed. By introducing the Markov Chain Monte Carlo (MCMC) and the Euclidean distance， a new adaptive strategy for design of experiments (DoE)， considering the prediction uncertainty and the sampling uniformity， was developed to establish the Gaussian process classifier more efficiently. Furthermore， the quasi-optimal importance sampling density function was constructed by adopting the kernel density estimation (KDE). Based on the stability of failure probability estimation， a more accurate stopping criterion was also proposed. A piecewise function was utilized to verify the accuracy and efficiency of the proposed analysis method. The instability probability of a deep submergence ring stiffened pressure cylindrical shell structure obtained by the proposed method is about 8.242×10^-5.

Key words: instability probability, ring stiffened pressure cylindrical shell, Gaussian process classification (GPC), small failure probability, adaptive design of experiments