Direct probability integral method for stochastic response analysis of static and dynamic structural systems

Chen, Guohai; Yang, Dan

doi:10.1016/j.cma.2019.112612

Cited by 110 publications

(22 citation statements)

References 46 publications

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“…The probability density evolution method (PDEM) is an approach that can deal with the problem involving randomness simultaneously in structural parameters and stochastic excitations [4]. In the past decades, this method has been studied extensively and applied widely [33,34].…”

Section: Introductionmentioning

confidence: 99%

Globally-evolving-based generalized density evolution equation for nonlinear systems involving randomness from both system parameters and excitations

Chen

Lyu

2022

Proc. R. Soc. A.

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It has long been one of the main challenges in science and engineering to capture the probabilistic response of high-dimensional nonlinear stochastic dynamic systems involving double randomness, i.e. randomness in both system parameters and excitations. For this purpose, a globally-evolving-based generalized density evolution equation (GE-GDEE) is established. Generally, for a multi-dimensional nonlinear system involving double randomness, if one single physical quantity as a response of the system is of interest, a GE-GDEE, as a two-dimensional partial differential equation (PDE) governing the probability density function (PDF), can be derived. The effective drift coefficients, which represent the physically driving force function in the GE-GDEE, can be determined based on the data from some representative deterministic dynamic analyses of the underlying physical system. A new estimator for effective drift coefficients is developed based on the vine copulas. Once the effective drift coefficients are determined, the GE-GDEE can be solved to capture the probability distributions of the quantities of interest. Several numerical examples, including linear and nonlinear multi-degree-of-freedom (MDOF) systems subjected to white noise or non-stationary earthquake ground motions, are presented to verify the effectiveness of the proposed method. Finally, problems for future investigations are discussed.

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Section: Introductionmentioning

confidence: 99%

Globally-evolving-based generalized density evolution equation for nonlinear systems involving randomness from both system parameters and excitations

Chen

Lyu

2022

Proc. R. Soc. A.

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“…Zhang et al [10] proposed an efficient method for time-variant reliability including finite element analysis. Chen and Yang [11] proposed a method called direct probability integral method; this method can calculate both static and dynamic reliability [12,13]. Another set of scholars studied the bearing capacity of concrete structures based on reliability theory; for example, Zhou et al [14] analyzed the capacity of FRP shear strengthened reinforced concrete beams.…”

Section: Introductionmentioning

confidence: 99%

Reliability Analysis of Concrete Beam with High-Strength Steel Reinforcement

2022

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In concrete structures, replacing conventional steel bars with high-strength steel reinforcement (HSSR) can effectively save the use of materials. However, the deformation properties and strength dispersion of HSSR are different from those of conventional steel reinforcement, which restricts or conservatively uses them in practical applications. For example, the partial safety factor of HRB500 grade steel bars (the yield strength is 500 MPa) in guideline GB50010-2010 is larger than that of conventional steel bars, and there is no relevant guidance for HRB600 grade steel bars (the yield strength is 600 MPa). Based on this, this paper will propose the limit state design method of high-strength steel reinforced concrete beam (HSSRCB) based on reliability analysis, which is convenient for the popularization and use of HSSR. Firstly, the flexural performance test of HSSRCBs was introduced, and the flexural capacity of HSSRCB was analyzed based on the existing prediction model. Second, a sectional numerical analysis model was established, where the section was discretized into several points, and then the curvature was gradually increased to obtain the corresponding bending moment through integration. A large number of samples were calculated to obtain statistical characteristics of the error of prediction model. Then, the limit state functions were established for two kinds of format, including partial safety factor format (PSSF) and resistance reduction factor format (RRFF), respectively, and the reliability of HSSRCBs was analyzed based on Monte Carlo simulation. Finally, the recommended values of partial safety factor of material and reduction factor of bearing capacity were proposed, in which the design strength of HRB500 and HRB600 reinforcement was 454 MPa and 545 MPa for PSSF, respectively, and the resistance reduction factor for the flexural capacity of HSSRCB was 0.8 and 0.75 for RRFF, respectively.

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“…Structural responses are uncertain owing to parameter uncertainties. Obtaining probability distributions and the first two statistical moments of responses and assessing reliability are the primary objectives of dynamic analysis of structures with uncertain parameters 3,4 . Monte Carlo simulation (MCS) is the most widely used method in uncertainty quantification (UQ) 5,6 .…”

Section: Introductionmentioning

confidence: 99%

“…Obtaining probability distributions and the first two statistical moments of responses and assessing reliability are the primary objectives of dynamic analysis of structures with uncertain parameters. 3,4 Monte Carlo simulation (MCS) is the most widely used method in uncertainty quantification (UQ). 5,6 As a sample-based method, its expensive computational effort dramatically limits its application in the UQ of complex engineering structures.…”

Section: Introductionmentioning

confidence: 99%

Nonstationary random vibration analysis of structures with uncertain parameters based on a polynomial dimensional decomposition

Liu

Zhao

2022

Earthq Engng Struct Dyn

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Based on polynomial dimensional decomposition (PDD), a novel method for analysing nonstationary random vibration of structures with uncertain parameters is proposed in this paper. The uncertain structural parameters are assumed to be independent random variables, with certain types of probability distributions; thus, the nonstationary random vibration responses of the structures become stochastic functions of these uncertain parameters. A dimensional decomposition and Fourier expansion were applied to calculate the statistical characteristics of the nonstationary random vibration responses of the structures. To calculate the conditional power spectral density (CPSD) and conditional standard deviation (CSD) of the nonstationary random vibration responses, CPSD and CSD were explicitly expressed using expansion coefficients and polynomial basis. Subsequently, the probability distributions of the structural responses can be effectively calculated in terms of these explicit expressions. Dimension-reduction integration and Gauss numerical integration were applied to calculate expansion coefficients. The validity of the proposed method was verified by numerical examples, including a single-degree-of-freedom system and a multi-degree-offreedom system (reinforced concrete shear wall). The results indicate that the proposed method is as accurate as Monte Carlo simulation (MCS), whereas the proposed method requires considerably smaller number of nonstationary random vibration analyses than MCS. Moreover, the nonstationary random vibration analysis of a long-span cable-stayed bridge demonstrates that the proposed method is feasible for quantifying the uncertainties of the nonstationary random vibration responses of complex engineering structures with uncertain parameters.

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Direct probability integral method for stochastic response analysis of static and dynamic structural systems

Cited by 110 publications

References 46 publications

Globally-evolving-based generalized density evolution equation for nonlinear systems involving randomness from both system parameters and excitations

Globally-evolving-based generalized density evolution equation for nonlinear systems involving randomness from both system parameters and excitations

Reliability Analysis of Concrete Beam with High-Strength Steel Reinforcement

Nonstationary random vibration analysis of structures with uncertain parameters based on a polynomial dimensional decomposition

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