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The evaluation of algorithms for determination of the reliability index

A. Dudzik U. Radoń
Archives of Civil Engineering | 2015 | No 3 | 133-147
Keywords random variables reliability index FORM method sensitivity of the reliability index stability dynamic analysis equilibrium path design point
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Abstract

The study deals with stability and dynamic problems in bar structures using a probabilistic approach. Structural design parameters are defined as deterministic values and also as random variables, which are not correlated. The criterion of structural failure is expressed by the condition of non-exceeding the admissible load multiplier and condition of non-exceeding the admissible vertical displacement. The Hasofer-Lind index was used as a reliability measure. The primary research tool is the FORM method. In order to verify the correctness of the calculations Monte Carlo and Importance Sampling methods were used. The sensitivity of the reliability index to the random variables was defined. The limit state function is not an explicit function of random variables. This dependence was determined using a numerical procedure, e.g. the finite element methods. The paper aims to present the communication between the STAND reliability analysis program and the KRATA and MES3D external FE programs.

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Authors and Affiliations

A. Dudzik
U. Radoń

Implicit neural state functions in hybrid reliability analysis of plane frame

Beata Potrzeszcz-Sut Agnieszka Dudzik Urszula Radoń
Archives of Civil Engineering | 2023 | vol. 69 | No 4 | 55-71 | DOI: 10.24425/ace.2023.147647
Keywords Hybrid FORM method limit state functions neural networks partial safety factors reliability analysis sensitivity
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Abstract

The objective of the article involves presenting innovative approach to the assessment of structural reliability analysis. The primary research method was the First Order Reliability Method (FORM). The Hasofer–Lind reliability index in conjunction with transformation method in the FORM was adopted as the reliability measure. The implicit limit state functions were used in the analysis. The formulation of the random variables functions were created in the Matlab software by means of neural networks (NNs). The reliability analysis was conducted in Comrel module of Strurel computing environment. In the proposed approach, Hybrid FORM method (HF) used the concept in which NNs replaced the polynomial limit state functions obtained from FEM (Finite Elements Method) for chosen limit parameters of structure work. The module Comrel referenced Matlab files containing limit state functions. In the reliability analysis of structure, uncertain and uncorrelated parameters, such us base wind speed, characteristic snow load, elasticity modulus for steel and yield point steel are represented by random variables. The criterion of structural failure was expressed by four limit state functions – two related to the ultimate limit state and two related to the serviceability limit state. Using module Comrel values of the reliability index with the FORM method were determined. Additionally, the sensitivity of the reliability index to random variables and graph of partial safety factors were described. Replacing the FEM program by NNs significantly reduces the time needed to solve the task. Moreover, it enables the parallel formulation of many limit functions without extending the computation time.
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Authors and Affiliations

Beata Potrzeszcz-Sut
1
ORCID: ORCID
Agnieszka Dudzik
1
ORCID: ORCID
Urszula Radoń
1
ORCID: ORCID
  1. Kielce University of Technology, Faculty of Civil Engineering and Architecture, al. Tysiaclecia Panstwa Polskiego 7, 25-314 Kielce, Poland

Influence of random character of reinforcement cover in bending elements

Katarzyna Sieńkowska Lidia Buda-Ożóg
Archives of Civil Engineering | 2021 | vol. 67 | No 4 | 123-137 | DOI: 10.24425/ace.2021.138490
Keywords reinforced structures reliability index bending FEM analysis FORM method Monte Carlo simulation
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Abstract

The paper presents the assessment of reliability depending on the reinforcement cover thickness for elements subject to bending. Based on the experimental tests of 12 reinforced concrete beams subjected to four-point bending the numerical model was validated. In the next steps this numerical model was used for the Monte Carlo simulation. During the analyses the failure probability and the reliability index were determined by two methods – using probabilistic method –FORMand fully probabilistic method Monte Carlo with the use of variance reduction techniques by Latin hypercube sampling (LHS). The random character of input data – compressive strength of concrete, yield strength of steel and effective depth of reinforcement were assumed in the analysis. Non-parametric Spearman rank correlation method was used to estimate the statistical relationship between random variables. Analyses have shown a significant influence of the random character of effective depth on reliability index and the failure probability of bending elements.
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Bibliography

[1] ATENA, Program Documentation, Prague, 2014.
[2] L. Buda-Ozóg, “Diagnostics of technical condition of concrete elements using dynamic methods”, PhD thesis, Rzeszow University of Technology, Poland 2008 (in Polish).
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[17] S. Wolinski, “Probabilistyczne podstawy współczesnych norm projektowania”, Zeszyty Naukowe Politechniki Rzeszowskiej, vol. 58, pp. 269–288, 2011.

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Authors and Affiliations

Katarzyna Sieńkowska
1
ORCID: ORCID
Lidia Buda-Ożóg
1
ORCID: ORCID
  1. Rzeszów University of Technology, Faculty of Civil and Environmental Engineering and Architecture, Powstancow Warszawy 12, 35-859 Rzeszów, Poland

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