Importance sampling for randomly excited dynamical systems

Macke, Michael; Bucher, Christian

doi:10.1016/s0022-460x(03)00204-9

Cited by 40 publications

(15 citation statements)

References 19 publications

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“…It can be shown that an ideal control u *( t ) exists, which yields

Var ({\overset{true˜}{P}}_{F}) = 0

, but its construction requires the knowledge of P F , the very quantity being sought to be determined . The way forward would be to seek suboptimal controls u ( t ) , which help to reduce the sampling variance appreciably and not to seek the ideal situation of obtaining

Var ({\overset{true˜}{P}}_{F}) = 0

.…”

Section: Girsanov Transformation In Computational Reliability Analysismentioning

confidence: 99%

Random vibration testing with controlled samples

Sundar

Manohar

2014

Struct. Control Health Monit.

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SUMMARY This paper proposes a novel experimental test procedure to estimate the reliability of structural dynamical systems under excitations specified via random process models. The samples of random excitations to be used in the test are modified by the addition of an artificial control force. An unbiased estimator for the reliability is derived based on measured ensemble of responses under these modified inputs based on the tenets of Girsanov transformation. The control force is selected so as to reduce the sampling variance of the estimator. The study observes that an acceptable choice for the control force can be made solely based on experimental techniques and the estimator for the reliability can be deduced without taking recourse to mathematical model for the structure under study. This permits the proposed procedure to be applied in the experimental study of time‐variant reliability of complex structural systems that are difficult to model mathematically. Illustrative example consists of a multi‐axes shake table study on bending–torsion coupled, geometrically non‐linear, five‐storey frame under uni/bi‐axial, non‐stationary, random base excitation. Copyright © 2014 John Wiley & Sons, Ltd.

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“…It can be shown that an ideal control u *( t ) exists, which yields

Var ({\overset{true˜}{P}}_{F}) = 0

Var ({\overset{true˜}{P}}_{F}) = 0

.…”

Section: Girsanov Transformation In Computational Reliability Analysismentioning

confidence: 99%

Random vibration testing with controlled samples

Sundar

Manohar

2014

Struct. Control Health Monit.

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show abstract

“…Estimate coefficients A and B of (1) using constructed set of (f, b(f)) by regression analysis. In order to put equal weights on all support points in regression analysis (2) may be used instead of (1) bðf…”

Section: Asymptotic Samplingmentioning

confidence: 99%

“…These methods tackle this problem from very different points of view i.e. importance sampling [1,2] moves the sampling density function to the boundaries of the failure domain, directional sampling [3] tries to find the boundaries of the limit state function G(X) in different directions of the random variables within the U-space. Here primarily the original random variables of the limit state function, X, with joint probability distribution function F X (x) are transformed into the standard normally distributed random variables U, the domain of which is called the U-space, using the Rosenblatt transformation T: X ?…”

Section: Introductionmentioning

confidence: 99%

Applications of asymptotic sampling on high dimensional structural dynamic problems

2011

Self Cite

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“…On passing, it should be noted that GAs utilize only the numerical values of the objective function and its associated constraints for the evaluation of the chromosome fitness, as seen from Eqs. (3)(4)(5). This advantage makes GAs readily applicable to real-world problems where the limit state functions are generally implicit with respect to random variables.…”

Section: Chromosome Representation and Selection Processmentioning

confidence: 99%

“…Classical optimization techniques like non-linear programming or gradient-based technique can be employed for the purpose [3,4]. However, such optimization techniques belong to the class of single-point-based search [5].…”

Section: Introductionmentioning

confidence: 99%