Response probability density function for multi-cracked beams with uncertain amplitude and position of cracks

Laudani, Rossella; Falsone, G.

doi:10.1016/j.apm.2021.06.005

Cited by 12 publications

(3 citation statements)

References 37 publications

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“…When sufficient samples are provided, the accurate PDF of these random variables can be easily procured to quantify their uncertainties. There are a variety of probability distributions widely adopted in engineering practices, including Gaussian, Poisson, and Weibull distributions [16][17][18][19]. For multidimensional random variables, the easy-to-procure incomplete information such as statistical moments and marginal probability distributions, instead of the precise joint probability distribution, is often exploited to measure the randomness of parameters.…”

Section: Probabilistic Modelsmentioning

confidence: 99%

Recent Advances in Surrogate Modeling Methods for Uncertainty Quantification and Propagation

Wang

Qiang

et al. 2022

Symmetry

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Surrogate-model-assisted uncertainty treatment practices have been the subject of increasing attention and investigations in recent decades for many symmetrical engineering systems. This paper delivers a review of surrogate modeling methods in both uncertainty quantification and propagation scenarios. To this end, the mathematical models for uncertainty quantification are firstly reviewed, and theories and advances on probabilistic, non-probabilistic and hybrid ones are discussed. Subsequently, numerical methods for uncertainty propagation are broadly reviewed under different computational strategies. Thirdly, several popular single surrogate models and novel hybrid techniques are reviewed, together with some general criteria for accuracy evaluation. In addition, sample generation techniques to improve the accuracy of surrogate models are discussed for both static sampling and its adaptive version. Finally, closing remarks are provided and future prospects are suggested.

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Section: Probabilistic Modelsmentioning

confidence: 99%

Recent Advances in Surrogate Modeling Methods for Uncertainty Quantification and Propagation

Wang

Qiang

et al. 2022

Symmetry

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show abstract

“…In ref. [28], an implementation of the ramp function to a fundamental problem of fracture mechanics concerning multi-cracked simply supported beams was carried out, where the determination of the response of the beams was addressed under static loads and in the presence of multiple cracks, whilst in ref. [29], a substructure elimination method for evaluating the bending vibration of beams was performed.…”

Section: Introductionmentioning

confidence: 99%

An Explicit Form of Ramp Function

Venetis

2024

AppliedMath

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In this paper, an analytical exact form of the ramp function is presented. This seminal function constitutes a fundamental concept of the digital signal processing theory and is also involved in many other areas of applied sciences and engineering. In particular, the ramp function is performed in a simple manner as the pointwise limit of a sequence of real and continuous functions with pointwise convergence. This limit is zero for strictly negative values of the real variable x, whereas it coincides with the independent variable x for strictly positive values of the variable x. Here, one may elucidate beforehand that the pointwise limit of a sequence of continuous functions can constitute a discontinuous function, on the condition that the convergence is not uniform. The novelty of this work, when compared to other research studies concerning analytical expressions of the ramp function, is that the proposed formula is not exhibited in terms of miscellaneous special functions, e.g., gamma function, biexponential function, or any other special functions, such as error function, hyperbolic function, orthogonal polynomials, etc. Hence, this formula may be much more practical, flexible, and useful in the computational procedures, which are inserted into digital signal processing techniques and other engineering practices.

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“…In Ref. [28] an implementation of Ramp Function to a fracture mechanics problem concerning multi-cracked simply supported beams is carried out where the determination of the response of beams is addressed under static loads and in presence of multiple cracks, whilst in Ref. [29] a substructure elimination method for evaluating bending vibration of beams is performed.…”

Section: Introductionmentioning

confidence: 99%

An Explicit Form of Ramp Function

Venetis

2023

Preprint

View full text Add to dashboard Cite

In this paper, an analytical form of Rump Function is presented. This seminal function constitutes a fundamental concept of digital signal processing theory and is also involved in many other areas of applied mathematics. In particular, Rump Function is performed in a simple manner as the limit of a sequence of real functions letting ? tend to infinity. This limit is zero for strictly negative values of the real variable ? whereas it coincides with the independent variable ? for strictly positive values of the variable ?. The novelty of this work compared to other research studies concerning analytical expressions of the Ramp Function, is that the proposed formula is not exhibited in terms of miscellaneous special functions, e.g. Gamma Function, Biexponential Function or any other special functions such as Error Function, Hyperbolic Function, Orthogonal polynomials etc. Hence, this formula may be much more practical, flexible and useful in the computational procedures which are inserted into digital signal processing techniques and other engineering practices.

show abstract

Response probability density function for multi-cracked beams with uncertain amplitude and position of cracks

Cited by 12 publications

References 37 publications

Recent Advances in Surrogate Modeling Methods for Uncertainty Quantification and Propagation

Recent Advances in Surrogate Modeling Methods for Uncertainty Quantification and Propagation

An Explicit Form of Ramp Function

An Explicit Form of Ramp Function

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