Presentation: Dr. Mengze Lyu

Physically-Driven Probability Density Evolution Equations for Uncertainty Propagation and Reliability Analysis, August 1, 1:00 pm, room 116


Uncertainty propagation and reliability analysis in complex nonlinear stochastic dynamical systems are significant challenges in the fields of science and engineering. The randomness of system parameters and external excitations significantly influences the system dynamic behavior with complex nonlinearity. For arbitrary path-continuous response of interest in complex systems, a governing equation for the transient probability density function (PDF) can be established, known as the dimension-reduced probability density evolution equation (DR-PDEE). When considering a single response, the DR-PDEE becomes a one- or two-dimensional partial differential equation (PDE), where the intrinsic drift functions are the key physical drivers responsible for uncertainty propagation. For solving joint PDFs of multiple response quantities, a decoupled multi-dimensional probability density evolution method has been developed, which avoids the need to solve high-dimensional PDEs and provides numerical solutions for the joint PDF of multiple responses. Furthermore, to achieve the first-passage reliability of high-dimensional systems, the DR-PDEE with an absorbing boundary process has been developed with an accurate and efficient numerical implementation. Additionally, the time-variant extreme value process is introduced for first-passage problem, establishing a probability evolution integral equation for the time-variant extreme value distribution (EVD) of Markov processes and proposing an augmented Markov vector method for numerically solving time-variant EVDs. Numerical examples demonstrate that the uncertainty propagation and reliability analysis methods based on probability density evolution equations exhibit high numerical accuracy, particularly in capturing the small probability of failure in rare events and the complex features in the true response PDFs, such as jumps, concentrated probabilities, and tail information. Finally, this research showcases several applications of the probability density evolution analysis in various engineering scales, including stochastic discrete element method of particle material representative volume elements, stochastic phase field modeling of quasi-brittle component fracture behavior with multivariate dependent random fields, seismic reliability of high-rise reinforced concrete shear wall structures, and wind-hazard fragility of building envelopes under the random impact of windborne debris.


Speaker information

Meng-Ze Lyu (律梦泽)
Ph.D., Postdoctoral Fellow
College of Civil Engineering, Tongji University, Shanghai, China



Dr. Meng-Ze Lyu (born in 1994) is a Postdoctoral Fellow at the College of Civil Engineering, Tongji University. He obtained his B.Sc. (2015), M.Eng. (2017), and Ph.D. (2022) degrees from Tongji University. His primary research focus lies in stochastic dynamics and reliability analysis. Dr. Lyu’s investigations include the development of dimension-reduced probability density evolution equation (DR-PDEE) for probabilistic responses and reliability analysis of high-dimensional nonlinear stochastic dynamical systems, the analytical and numerical methods for the time-variant extreme value distribution of Markov processes, and the applications in structural seismic safety assessment and wind-hazard fragility analysis. Dr. Lyu has authored a translated book and published 12 journal papers in English, 2 journal papers in Chinese, and 10 conference full papers. He was selected for the Shanghai Post-Doctoral Excellence Program in 2022.

Selected publications of Dr. Meng-Ze Lyu include:

  1. Lyu MZ, Ai XQ, Sun TT, Chen JB, 2023. Fragility analysis of curtain walls based on wind-borne debris considering wind environment. Probab Eng Mech, 71: 103397.
  2. Lyu MZ, Chen JB, 2022. A unified formalism of the GE-GDEE for generic continuous responses and first-passage reliability analysis of multi-dimensional nonlinear systems subjected to non-white-noise excitations. Struct Saf, 98: 102233.
  3. Lyu MZ, Chen JB, 2021. First-passage reliability of high-dimensional nonlinear systems under additive excitation by the ensemble-evolving-based generalized density evolution equation. Probab Eng Mech, 63: 103119.
  4. Lyu MZ, Wang JM, Chen JB, 2021. Closed-form solutions for the probability distribution of time-variant maximal value processes for some classes of Markov processes. Commun Nonlinear Sci Numer Simulat, 99: 105803.
  5. Lyu MZ, Chen JB, Pirrotta A, 2020. A novel method based on augmented Markov vector process for the time-variant extreme value distribution of stochastic dynamical systems enforced by Poisson white noise. Commun Nonlinear Sci Numer Simulat, 80: 104974.


Additional information

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