PDEM-based dimension-reduction of FPK equation for additively excited hysteretic nonlinear systems

Chen, Jianbing; Yuan, Shurong

doi:10.1016/j.probengmech.2014.05.002

Cited by 20 publications

(3 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For comparison, the non-resonance response of the same system is also given below (see Figs. [14][15]. Fig.…”

Section: Jump and Bifurcationmentioning

confidence: 98%

“…On the other hand, many approximate methods have been proposed for predicting the response of the hysteretic system exposed to random excitations. They are the methods of equivalent linearization [7][8][9][10][11], explicit time-domain method [12], probability density evolution method [13][14], Gaussian closure technique [15], exponential-polynomial closure (EPC) method [16][17], dissipation energy balancing method [18], stochastic averaging [19][20][21][22][23][24][25][26], deep neural networks [27], Monte Carlo simulation [28], etc. Among methods mentioned above, the stochastic averaging method has the remarkable advantages in simplifying the equation of motion while retaining the main nonlinear behavior of system [29].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stationary Response of Flag-shaped Hysteretic System under Combined Harmonic and White Noise Excitations

Chen¹,

Hu²,

Ye³

2021

Preprint

View full text Add to dashboard Cite

The dynamical system containing flag-shaped hysteretic behavior is common in practice. In this paper, the stationary response of flag-shaped hysteretic system excited by harmonic excitation as well as Gaussian white noise is determined with the technique of stochastic averaging. The reliability of the presented approach is demonstrated by relevant digital simulation. The stochastic jump under a certain combination of parameters is found. The stochastic P-bifurcation phenomenon, i.e., the disappearance or appearance of bimodal shape of stationary response, occurs concerning to the variation of system’s parameters. Besides, the response of the system exposed to only harmonic excitation or non-resonance case is also examined for comparison, respectively. The numerical results show that the stationary amplitude response displays typical “soft” system behavior, and the deterministic jump may occur under pure harmonic excitation. Moreover, the non-resonance response is always weaker than that of resonant case.

show abstract

“…For comparison, the non-resonance response of the same system is also given below (see Figs. [14][15]. Fig.…”

Section: Jump and Bifurcationmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Stationary Response of Flag-shaped Hysteretic System under Combined Harmonic and White Noise Excitations

Chen¹,

Hu²,

Ye³

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…However, some advances have been made based on this thought. For instance, the FPK equation could be reduced to a lower-dimensional partial differential equation [17].…”

Section: The Generalized F-discrepancy (Gf-discrepancy)mentioning

confidence: 99%

Probability Density Evolution Analysis of Seismic Response of Nonlinear Structures With Random Parameters

Yang¹,

Chen²,

Li³

2015

Proceedings of the 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering (UNCECO

Self Cite

View full text Add to dashboard Cite

Abstract. The performance and reliability of engineering structures under extreme disastrous dynamic excitations (e.g. earthquakes) is of great concern due to the strong nonlinear mechanical behaviors as well as the uncertainty involved in both structural properties and external excitations. Great efforts have been devoted into this field in the past INTRODUCTIONDue to the randomness of the time and magnitude of earthquakes, it is possible for all the practical engineering structures to enter the phase of exhibiting nonlinear behaviors [1,2]. Therefore, it is of great importance to take into account the coupling of nonlinearity and randomness in assessing the performance and reliability of a practical structure rationally. In the past few decades, though the stochastic dynamics of structures, including the random vibration and the stochastic structural analysis, was extensively investigated, yielding a variety of approaches such as the Monte Carlo simulation (MCS) [3], the random perturbation method [4,5], and the orthogonal polynomials expansion [6,7], ect., great challenges are still encountered in the stochastic dynamical analysis of nonlinear structures of practical engineering interest [8]. Moreover, these methods are mainly aimed at obtaining the first second order statistics of structural responses rather than higher order statistics or probability density functions, which are of crucial importance in the reliability evaluation of nonlinear structures [9,10]. From the perspective of physical stochastic systems, a family of probability density evolution method (PDEM), which is capable of capturing the instantaneous probability density functions of stochastic responses of nonlinear structures, has been developed by Li and Chen in the past decade [11]. Based on the random event description of principle of preservation of probability, a generalized density evolution equation (GDEE), of which the dimension is free from the dimension of the original dynamical system, is derived and solved by incorporating the embedded physical equations [12].Two possible paths, i.e., the ensemble evolution path and the point evolution path, could be employed in the numerical solution of PDEM [12]. In the point evolution based approach, a smart selection of representative points is of paramount importance. Great endeavors have been devoted into the optimal selection of representative point set [13,14]. In the present paper, the generalized F-discrepancy (GF-discrepancy) is employed in the determination of representative points. A numerical example of a nonlinear frame-shear structure is presented. The stochastic seismic responses and the corresponding probabilistic information, including probability density functions, are obtained and analyzed. Then the evaluation of reliabilities under different threshold levels are carried out so that the accuracy and efficiency of PDEM could be verified. Problems to be further studied are discussed.

show abstract

An efficient method for statistical moments and reliability assessment of structures

Kong

2018

Struct Multidisc Optim

View full text Add to dashboard Cite

PDEM-based dimension-reduction of FPK equation for additively excited hysteretic nonlinear systems

Cited by 20 publications

References 26 publications

Stationary Response of Flag-shaped Hysteretic System under Combined Harmonic and White Noise Excitations

Stationary Response of Flag-shaped Hysteretic System under Combined Harmonic and White Noise Excitations

Probability Density Evolution Analysis of Seismic Response of Nonlinear Structures With Random Parameters

An efficient method for statistical moments and reliability assessment of structures

Contact Info

Product

Resources

About