Determination of parameters range in rock engineering by means of Random Set Theory

Tonon, Fulvio; Bernardini, Alberto; Mammino, Armando

doi:10.1016/s0951-8320(00)00058-2

Cited by 93 publications

(40 citation statements)

References 25 publications

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“…Therefore, if a variability interval of an uncertain parameter (β±β·µ, with β expressed in percentage terms) is identified, it is possible to evaluate the standard deviation σ of the probabilistic distribution of the population in the following way: σ = (β·µ)/3. Once the probabilistic distributions of each parameter of the problem have been determined (through µ and σ), it is possible to proceed with a random extraction of these parameters using the Monte-Carlo method (Karakostas and Manolis, 2000;Oreste, 2005a;Fellin et al, 2010;Oreste, 2006;Tonon et al, 2000).…”

Section: Methodsmentioning

confidence: 99%

“…In order to be able to conduct a probabilistic type analysis, it is generally necessary to refer to the Monte-Carlo method, which allows the single uncertain calculation parameters to be extracted randomly, once their probabilistic distribution has been defined (type of distribution, mean value and standard deviation for each parameter considered uncertain) (Oreste, 2006;Tonon et al, 2000).…”

Section: Introductionmentioning

confidence: 99%

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Analysis of the Tunnel-Support Interaction Through a Probabilistic Approach

Oreste¹

2015

American Journal of Applied Sciences

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The analysis of the behavior of a tunnel requires the evaluation of numerous parameters, relative to the ground and the support structure and which are generally only known with a certain degree of approximation. The uncertainty of these parameters is reflected on the results of the calculation, that is, on the state of stress in the support structure. In order to be able to manage this uncertainty on the representative ground and support structure parameters in a rational way, it is useful to resort to a probabilistic type analysis, making use of the MonteCarlo method and to simple analytical methods for an analysis of the tunnel-support structure interaction. A calculation procedure of probabilistic type that is able to establish representative values of the maximum moment and of the associated normal force in the support structure is presented in this study. This procedure can be used to verify the suitability of the support structure to sustain the induced loads.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis of the Tunnel-Support Interaction Through a Probabilistic Approach

Oreste¹

2015

American Journal of Applied Sciences

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“…In this interpretation, a fuzzy set is a model of ambiguity and not of vagueness [24]. Let us extend the possibility distribution π F (u) by taking into account the restriction of N .…”

Section: Extended Possibility Distributionmentioning

confidence: 99%

Extensions of belief functions and possibility distributions by using the imprecise Dirichlet model

Utkin¹

2005

Fuzzy Sets and Systems

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“…The lower P (A i ) and upper probabilities P (A i ), computed in accordance with the imprecise Dirichlet model, are shown in Table 3. According to [22] …”

Section: Yρ(y)dymentioning

confidence: 99%

Probabilities of judgments provided by unknown experts by using the imprecise Dirichlet model

Utkin¹

2004

Risk, Decision and Policy

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Most models of aggregating expert judgments assume that there is available some information characterizing the experts. This information may be incorporated into hierarchical uncertainty models (second-order models). However, very often we do not know anything about experts or it is difficult to evaluate their quality. In this case, beliefs to experts may be in the interval [0,1] and the resulting assessments become to be non-informative. Moreover, attempts to assign some weights or beliefs to experts were not crowned with success because the behavior of experts may be distinguished in different circumstances. Therefore, this paper proposes to estimate expert judgments instead of experts themselves and studies how to assign interval probabilities of expert judgments by using the multinomial model.

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Determination of parameters range in rock engineering by means of Random Set Theory

Cited by 93 publications

References 25 publications

Analysis of the Tunnel-Support Interaction Through a Probabilistic Approach

Analysis of the Tunnel-Support Interaction Through a Probabilistic Approach

Extensions of belief functions and possibility distributions by using the imprecise Dirichlet model

Probabilities of judgments provided by unknown experts by using the imprecise Dirichlet model

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