Persian Curve Versus Monte Carlo Method

Ranjbaran, Abdolrasoul; Ranjbaran, Mohammad; Ranjbaran, Fatema

doi:10.3844/sgamrsp.2021.234.246

Cited by 3 publications

(1 citation statement)

References 13 publications

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“…The gainful practice in measuring uncertainties is the application of the probability concept (Hu¨llermeier and Waegeman, 2021). In this regard, the implementation of Monte Carlo Simulation (MCS) in practical reliability analyses involves sampling, and therefore, the results obtained will entail sampling errors (Menz et al, 2021;Ranjbaran et al, 2021). These errors decrease with increasing sampling size, but increasing sample size to achieve higher precision generally connotes an increase in computer time to generate random numbers and for data processing (O ¨kten and Liu, 2021).…”

Section: Introductionmentioning

confidence: 99%

Probabilistic reliability analysis for active vibration control of piezoelectric laminated composite plates using mesh-free finite volume method

Badeleh

Fallah

2022

Journal of Intelligent Material Systems and Structures

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The implementation of deterministic design approaches in the presence of uncertainty is an adequate design task. Probabilistic methods are then used in structural design procedures, offering structural safety predictions. In this study, reliability-based analysis of a piezoelectric laminated composite plate subjected to the mechanical loads was investigated, accounting for the epistemic source of uncertainty. Material properties of the plate were considered temperature-dependent. The sophisticated mesh-free finite volume approach was employed to actively control the vibration of the temperature-dependent piezoelectric laminated composite plate through the first-order shear deformation principles. The induced vibration was treated as a non-stationary random process, and the generalized failure index was estimated using the first-passage probability concept by adopting the novel asymptotic sampling technique. The veracity of the suggested model was corroborated by alternate approaches in the literature, comprising the finite element approach. Furthermore, the temperature-dependent piezoelectric laminated composite plate with different ply orientations was considered to assess the safety index variation against changes in the ambient temperature and the laminate stacking orientation. The obtained results revealed that with increasing temperature, the reliability of the composite plate reduced. It was also realized that the reliability index is directly correlated with the piezoelectric voltage.

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Section: Introductionmentioning

confidence: 99%

Probabilistic reliability analysis for active vibration control of piezoelectric laminated composite plates using mesh-free finite volume method

Badeleh

Fallah

2022

Journal of Intelligent Material Systems and Structures

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Persian Probability Function: An Alternative to Classical Probability Function

Ranjbaran

et al. 2022

NEDJR

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This paper presents the details of an analytical investigation which was carried out to propose Persian curve. The curve provides an alternative of probability functions to define the state of a system. The Persian curves are super functions of the state variable which includes state functions and two control parameters. The state variable is a scaled identification parameter of a system. The state functions are two specific functions of the state variable. The control parameters are determined from the real-world data. Since the Persian curve has the basic properties of the probability function, it is called the Persian probability function. It is concluded that all natural phenomena are certain and the lack of knowledge has led the humans to divide the phenomena into certain and stochastic categories. The proposed Persian curve was validated by analysing the probability data from different fields of study.

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Novel Approaches for Addressing Epistemic Uncertainty in Fracture Mechanics

Ranjbaran,

Ranjbaran

et al. 2024

NEDJR

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This paper presents a novel optimisation approach for analysing cracked structural systems, consisting of four key steps. The first step (called the Golden Derivative) derives an equation at the discontinuity specific to cracked systems. The cracked system is transformed into an equivalent intact system for analysis in the second step. The third step converts the unique cracked system equation into a finite element equation, revealing epistemic uncertainty that leads to the formulation of Persian curves (PCs). These curves are developed using the following three methods: numerical experimentation, equivalent springs and logical reasoning, with consistent outcomes validating their effectiveness. The uncertainty is linked to the crack effect equation from fracture mechanics in the final step. It is shown by applying mathematical differentiation that this crack effect and classical fracture mechanics inherently involve epistemic uncertainty. A proposed remedy addresses this issue. The derivation of PC is based on pure mathematics and logical reasoning (bridging probabilistic and deterministic methods) making the results applicable across various fields for analysing real-world data.

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Persian Curve Versus Monte Carlo Method

Cited by 3 publications

References 13 publications

Probabilistic reliability analysis for active vibration control of piezoelectric laminated composite plates using mesh-free finite volume method

Probabilistic reliability analysis for active vibration control of piezoelectric laminated composite plates using mesh-free finite volume method

Persian Probability Function: An Alternative to Classical Probability Function

Novel Approaches for Addressing Epistemic Uncertainty in Fracture Mechanics

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