Direct probability integral method (DPIM)

Direct probability integral method (DPIM) is a unified framework for uncertainty propagation analysis, reliability analysis and design.

Direct probability integral method (DPIM) is a unified framework for uncertainty propagation analysis, reliability analysis and reliability-based optimization design for static or dynamic structural systems, which is based on the probability density integral equations (PDIEs) from the principle of conservation of probability.

DPIM_SDOF.m is for stochastic response analysis of SDOF system using DPIM;

SelectPoint_GF.m is for generating the representative point set (integration points) and calculating assigned probability (integration weight), so as to solve the probability density integral equation (PDIE) based on GF-discrepancy point selection technique.

Main references:

[1] G.H. Chen, D.X. Yang, Direct probability integral method for stochastic response analysis of static and dynamic structural systems, Computer Methods in Applied Mechanics and Engineering, 357 (2019) 112612. DOI:10.1016/j.cma.2019.112612

[2] G.H. Chen, D.X. Yang, A unified analysis framework of static and dynamic structural reliabilities based on direct probability integral method, Mechanical Systems and Signal Processing, 158 (2021) 107783. DOI: 10.1016/j.ymssp.2021.107783

[3] G.H. Chen, D.X. Yang, Y.H. Liu, H.C. Guo. System reliability analysis of static and dynamic structures via direct probability integral method. Computer Methods in Applied Mechanics and Engineering, 388 (2022) 114262. DOI: 10.1016/j.cma.2021.114262