Fatigue Life Analysis of Vehicle Systems under Non-Gaussian Excitation

Fatigue life analysis is an important work in manufacturing of vehicle systems. The traditional method is to assume that stochastic loads are Gaussian type, then fatigue life is calculated by rain-flow counting, S-N curve and Miner linear damage rule. However, it is difficult to acquire accurate results by this means. In this paper, a numerical methodology is used to simulate non-Gaussian loads considering effects of skewness and kurtosis, as well as to estimate fatigue life under non-Gaussian stresses. Firstly, non-Gaussian inputs are represented by polynomial chaos expansion (PCE) and Karhunen-Loeve (KL) expansion when they are characterised using first four moments, i.e. mean, variance, skewness, kurtosis and a given correlation structure. During this process, we propose spectral decomposition to eliminate the influence of potential imaginary numbers, principal component analysis is also proposed to simplify calculating procedure in KL. Besides, original Monte Carlo sampling is replaced by quasi Monte-Carlo (QMC), which could greatly reduce the workload of numerical simulations. In order to get first four moments and correlation structure of outputs, differential equations of motion are numerically integrated by Runge-Kutta method. Meanwhile, response trajectories are represented based on PCE-KL-QMC approach. Eventually, the rain-flow counting is applied into these trajectories to obtain fatigue life variables, and a convenient formula about the saddlepoint approximations (SPA) represented by first four moments is proposed to provide fatigue life PDF. According to the above way, accurate and effective fatigue life estimation results can be presented

Download Full-text

Fatigue Life Analysis Under Non-Gaussian Random Vibration Excitation

10.1007/978-981-16-3694-3_5 ◽

2021 ◽

pp. 81-122

Author(s):

Yu Jiang ◽

Junyong Tao ◽

Xun Chen

Keyword(s):

Fatigue Life ◽

Random Vibration ◽

Vibration Excitation ◽

Life Analysis ◽

Fatigue Life Analysis ◽

Non Gaussian

Download Full-text

Reliability of Nonlinear Vibratory Systems Under Non-Gaussian Loads

Volume 2B: 43rd Design Automation Conference ◽

10.1115/detc2017-67313 ◽

2017 ◽

Author(s):

Vasileios Geroulas ◽

Zissimos P. Mourelatos ◽

Vasiliki Tsianika ◽

Igor Baseski

Keyword(s):

Duffing Oscillator ◽

Equations Of Motion ◽

Time Dependent ◽

Correlation Structure ◽

Output Process ◽

Quasi Monte Carlo ◽

Standard Normal ◽

Mc Simulation ◽

Non Gaussian ◽

First Four Moments

A general methodology is presented for time-dependent reliability and random vibrations of nonlinear vibratory systems with random parameters excited by non-Gaussian loads. The approach is based on Polynomial Chaos Expansion (PCE), Karhunen-Loeve (KL) expansion and Quasi Monte Carlo (QMC). The latter is used to estimate multi-dimensional integrals efficiently. The input random processes are first characterized using their first four moments (mean, standard deviation, skewness and kurtosis coefficients) and a correlation structure in order to generate sample realizations (trajectories). Characterization means the development of a stochastic metamodel. The input random variables and processes are expressed in terms of independent standard normal variables in N dimensions. The N-dimensional input space is space filled with M points. The system differential equations of motion are time integrated for each of the M points and QMC estimates the four moments and correlation structure of the output efficiently. The proposed PCE-KL-QMC approach is then used to characterize the output process. Finally, classical MC simulation estimates the time-dependent probability of failure using the developed stochastic metamodel of the output process. The proposed methodology is demonstrated with a Duffing oscillator example under non-Gaussian load.

Download Full-text

Reliability Analysis of Nonlinear Vibratory Systems Under Non-Gaussian Loads

Journal of Mechanical Design ◽

10.1115/1.4038212 ◽

2017 ◽

Vol 140 (2) ◽

Cited By ~ 6

Author(s):

Vasileios Geroulas ◽

Zissimos P. Mourelatos ◽

Vasiliki Tsianika ◽

Igor Baseski

Keyword(s):

Duffing Oscillator ◽

Equations Of Motion ◽

Time Dependent ◽

Correlation Structure ◽

Output Process ◽

Quasi Monte Carlo ◽

Standard Normal ◽

Non Gaussian ◽

First Four Moments ◽

Multidimensional Integrals

A general methodology is presented for time-dependent reliability and random vibrations of nonlinear vibratory systems with random parameters excited by non-Gaussian loads. The approach is based on polynomial chaos expansion (PCE), Karhunen–Loeve (KL) expansion, and quasi Monte Carlo (QMC). The latter is used to estimate multidimensional integrals efficiently. The input random processes are first characterized using their first four moments (mean, standard deviation, skewness, and kurtosis coefficients) and a correlation structure in order to generate sample realizations (trajectories). Characterization means the development of a stochastic metamodel. The input random variables and processes are expressed in terms of independent standard normal variables in N dimensions. The N-dimensional input space is space filled with M points. The system differential equations of motion (EOM) are time integrated for each of the M points, and QMC estimates the four moments and correlation structure of the output efficiently. The proposed PCE–KL–QMC approach is then used to characterize the output process. Finally, classical MC simulation estimates the time-dependent probability of failure using the developed stochastic metamodel of the output process. The proposed methodology is demonstrated with a Duffing oscillator example under non-Gaussian load.

Download Full-text