Research on Probability Density Estimation Method for Random Dynamic Systems

niyanrong666@126.com In this paper, the author researches on probability density estimation method for random dynamic systems. It indicate that, the Probability Density Function (PDF) curves and failure probabilities of stochastic systems with disjoint failure domains, multiple design points and discontinuous response are calculated effectively and accurately. Moreover, the Probability Density Estimation Method (PDEM) has much higher efficiency, and is a potential and general approach to attack the reliability analysis of complicated problems. Subsequently, the uncertainty propagation and dynamic reliability analysis of nonlinear random system under non-stationary excitations are addressed. The first passage failure criterion and stochastic harmonic function of power spectrum density model of non-stationary random process for earthquake action are utilized. The PDEM can achieve efficiently and accurately the dynamic response, transient PDF and reliability of nonlinear systems. Static and dynamic reliability analysis and uncertainty propagation of nonlinear stochastic structure are important research topics for domestic and abroad scholars, which have wide application prospect in engineering practice, and provide a solid theoretical basis for reliability design of the large scale and complex structure. Hong (2013) extends the use of probability density evolution method (PDEM) into the reliability analysis of nonlinear stochastic structures with complex performance functions, and dynamic response and reliability analysis of nonlinear structure under non-stationary excitations. Meanwhile, the influence mechanism of stochastic uncertainty propagation is investigated. In reliability analysis and optimal design of structures, there exist some complex limit state functions with failure domain separation, multiple design points and discontinuous response etc. For such kind of reliability analysis of structures with complex limit state functions, FORM and SORM which are widely used and highly efficient become fail. Despite the numerical simulation methods (such as Monte Carlo simulation, subset simulation and line sampling etc.) can solve this problem, but their computational efficiency is quite low. In addition, there is no accurate and efficient computing approach to address the random dynamic response and reliability analysis of nonlinear structures subject to non-stationary excitations. In recent years, Liu (2013) proposed the probability density evolution method which provides a unified solution framework for random vibration and reliability analysis of nonlinear structures. In this paper, the PDEM is applied to solve the difficult and important research subject of reliability analysis of structures with complicated limit state functions and uncertainty propagation. Actually, PDEM can obtain the probability density function of random structures under static and dynamic load, and is independent of any form of explicit and implicit limit state functions. This is the so-called Curse of Dimensionality. So, in order to effectively analyses high dimensionality data, it is a pivotal step to reduce their dimensional members. Yang’s (2013) paper is to explore a new feature selection way and propose a feature ranking method to reduce feature’s dimensionalities. In his paper, the principle of reducing feature’s dimensionalities is briefly introduced, and the principal ways of feature dimensionality reduction is reviewed. Moreover, the Probability Density Estimation Method (PDEM) has much higher efficiency than the Monte Carlo simulation, and is a potential and general approach to attack the reliability analysis of complicated problems. a novel feature ranking approach is proposed. A simplified approach is introduced to deal with unsupervised data. At last, the algorithm proposed in his paper is realized by MATLAB, and many DOI: 10.3303/CET1651213