Time-Dependent Reliability Estimation for Dynamic Systems Using a Random Process Approach

Time-dependent reliability is the probability that a system will perform its intended function successfully for a specified time. Unless many and often unrealistic assumptions are made, the accuracy and efficiency of time-dependent reliability estimation are major issues which may limit its practicality. Monte Carlo simulation (MCS) is accurate and easy to use but it is computationally prohibitive for high dimensional, long duration, time-dependent (dynamic) systems with a low failure probability. This work addresses systems with random parameters excited by stochastic processes. Their response is calculated by time integrating a set of differential equations at discrete times. The limit state functions are therefore, explicit in time and depend on time-invariant random variables and time-dependent stochastic processes. We present an improved subset simulation with splitting approach by partitioning the original high dimensional random process into a series of correlated, short duration, low dimensional random processes. Subset simulation reduces the computational cost by introducing appropriate intermediate failure sub-domains to express the low failure probability as a product of larger conditional failure probabilities. Splitting is an efficient sampling method to estimate the conditional probabilities. The proposed subset simulation with splitting not only estimates the time-dependent probability of failure at a given time but also estimates the cumulative distribution function up to that time with approximately the same cost. A vibration example involving a vehicle on a stochastic road demonstrates the advantages of the proposed approach.

Download Full-text

A Random Process Metamodel for Time-Dependent Reliability of Dynamic Systems

Volume 2A: 40th Design Automation Conference ◽

10.1115/detc2014-34313 ◽

2014 ◽

Author(s):

Dorin Drignei ◽

Igor Baseski ◽

Zissimos P. Mourelatos ◽

Vijitashwa Pandey

Keyword(s):

Random Process ◽

Dynamic Systems ◽

Random Variables ◽

Kriging Model ◽

Random Processes ◽

Time Dependent ◽

Total Probability ◽

Input And Output ◽

System Input ◽

Total Probability Theorem

A new metamodeling approach is proposed to characterize the output (response) random process of a dynamic system with random variables, excited by input random processes. The metamodel is then used to efficiently estimate the time-dependent reliability. The input random processes are decomposed using principal components or wavelets and a few simulations are used to estimate the distributions of the decomposition coefficients. A similar decomposition is performed on the output random process. A Kriging model is then built between the input and output decomposition coefficients and is used subsequently to quantify the output random process corresponding to a realization of the input random variables and random processes. In our approach, the system input is not deterministic but random. We establish therefore, a surrogate model between the input and output random processes. The quantified output random process is finally used to estimate the time-dependent reliability or probability of failure using the total probability theorem. The proposed method is illustrated with a corroding beam example.

Download Full-text

Time-Dependent Reliability of Dynamic Systems Using Subset Simulation With Splitting Over a Series of Correlated Time Intervals

Journal of Mechanical Design ◽

10.1115/1.4027162 ◽

2014 ◽

Vol 136 (6) ◽

Cited By ~ 39

Author(s):

Zhonglai Wang ◽

Zissimos P. Mourelatos ◽

Jing Li ◽

Igor Baseski ◽

Amandeep Singh

Keyword(s):

Stochastic Processes ◽

Dynamic Systems ◽

Failure Probability ◽

Limit State ◽

Computational Cost ◽

Reliability Estimation ◽

Time Dependent ◽

Cumulative Distribution ◽

High Dimensional ◽

Subset Simulation

Time-dependent reliability is the probability that a system will perform its intended function successfully for a specified time. Unless many and often unrealistic assumptions are made, the accuracy and efficiency of time-dependent reliability estimation are major issues which may limit its practicality. Monte Carlo simulation (MCS) is accurate and easy to use, but it is computationally prohibitive for high dimensional, long duration, time-dependent (dynamic) systems with a low failure probability. This work is relevant to systems with random parameters excited by stochastic processes. Their response is calculated by time integrating a set of differential equations at discrete times. The limit state functions are, therefore, explicit in time and depend on time-invariant random variables and time-dependent stochastic processes. We present an improved subset simulation with splitting approach by partitioning the original high dimensional random process into a series of correlated, short duration, low dimensional random processes. Subset simulation reduces the computational cost by introducing appropriate intermediate failure sub-domains to express the low failure probability as a product of larger conditional failure probabilities. Splitting is an efficient sampling method to estimate the conditional probabilities. The proposed subset simulation with splitting not only estimates the time-dependent probability of failure at a given time but also estimates the cumulative distribution function up to that time with approximately the same cost. A vibration example involving a vehicle on a stochastic road demonstrates the advantages of the proposed approach.

Download Full-text

FORCED RESPONSE OF STRUCTURAL DYNAMIC SYSTEMS WITH LOCAL TIME-DEPENDENT STIFFNESSES

Journal of Sound and Vibration ◽

10.1006/jsvi.2000.3072 ◽

2000 ◽

Vol 237 (5) ◽

pp. 761-773 ◽

Cited By ~ 11

Author(s):

R. DELTOMBE ◽

D. MORAUX ◽

G. PLESSIS ◽

P. LEVEL

Keyword(s):

Local Time ◽

Dynamic Systems ◽

Forced Response ◽

Time Dependent ◽

Structural Dynamic

Download Full-text

A Time-Dependent Reliability Estimation Method Based on Gaussian Process Regression

Volume 2A: 44th Design Automation Conference ◽

10.1115/detc2018-86294 ◽

2018 ◽

Author(s):

Wang Han ◽

Xiaoling Zhang ◽

Xiesi Huang ◽

Haiqing Li

Keyword(s):

Machine Learning ◽

Mechanical System ◽

Physical Modeling ◽

Learning Algorithm ◽

Estimation Method ◽

Gaussian Process Regression ◽

Reliability Estimation ◽

Time Dependent ◽

Physics Of Failure ◽

Gear Transmission System

This paper presents a time-dependent reliability estimation method for engineering system based on machine learning and simulation method. Due to the stochastic nature of the environmental loads and internal incentive, the physics of failure for mechanical system is complex, and it is challenging to include uncertainties for the physical modeling of failure in the engineered system’s life cycle. In this paper, an efficient time-dependent reliability assessment framework for mechanical system is proposed using a machine learning algorithm considering stochastic dynamic loads in the mechanical system. Firstly, stochastic external loads of mechanical system are analyzed, and the finite element model is established. Secondly, the physics of failure mode of mechanical system at a time location is analyzed, and the distribution of time realization under each load condition is calculated. Then, the distribution of fatigue life can be obtained based on high-cycle fatigue theory. To reduce the calculation cost, a machine learning algorithm is utilized for physical modeling of failure by integrating uniform design and Gaussian process regression. The probabilistic fatigue life of gear transmission system under different load conditions can be calculated, and the time-varying reliability of mechanical system is further evaluated. Finally, numerical examples and the fatigue reliability estimation of gear transmission system is presented to demonstrate the effectiveness of the proposed method.

Download Full-text