PROBABILITY DENSITY EVOLUTION ANALYSIS OF NONLINEAR RESPONSE OF STRUCTURES WITH NON-UNIFORM RANDOM PARAMETERS

Chen Jianbing; Zhang Shenghan

doi:10.6052/0459-1879-13-174

Volume 46 Issue 1

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Chinese Journal of Theoretical and Applied Mechanics > 2014 > 46(1): 136-144. > DOI: 10.6052/0459-1879-13-174

Chen Jianbing, Zhang Shenghan. PROBABILITY DENSITY EVOLUTION ANALYSIS OF NONLINEAR RESPONSE OF STRUCTURES WITH NON-UNIFORM RANDOM PARAMETERS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(1): 136-144. DOI: 10.6052/0459-1879-13-174

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PROBABILITY DENSITY EVOLUTION ANALYSIS OF NONLINEAR RESPONSE OF STRUCTURES WITH NON-UNIFORM RANDOM PARAMETERS

State Key Laboratory of Disaster Reduction in Civil Engineering & School of Civil Engineering, Tongji University, Shanghai 200092, China

Funds: The project was supported by the National Natural Science Foundation of China (11172210) and the Shuguang Program of Shanghai City (11SG21).

Received Date: June 06, 2013
Revised Date: August 13, 2013

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The probability density evolution method (PDEM) provides a feasible approach for nonlinear stochastic response analysis of multi-degree-of-freedom systems. In the present paper, the point evolution, ensemble evolution and the partition of probability-assigned space are firstly revisited. The criterion for point selection is then explored. The concept of generalized F-discrepancy (GF-discrepancy), which avoids the NP-hard problem of computation, is introduced for random variables of general non-uniform, non-Gaussian distribution as an index to measure the quality of a point set. The relationship between GF-discrepancy and EF-discrepancy is explored and the error bound is studied by the extended Koksma-Hlawka inequality. Based on the GF-discrepancy, a new strategy for point-selecting and space-partitioning is proposed. The numerical example shows that the proposed method enables highly accurate probability density evolution analysis of nonlinear structures involving dozens of non-uniform random variables. Problems to be further studied are discussed.
- nonlinear structures,
- stochastic response,
- probability density evolution method (PDEM),
- GF-discrepancy,
- Koksma-Hlawka inequality

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