International Journal of Nonlinear Analysis and Applications
Analysis of the structural reliability of dental filling under the effect of mouthwash G.U.M
Document Type : Research Paper
Authors
1 College of Health and Medical Technology - Baghdad, Middle Technical University, Iraq
2 College of Administration and Economics, Department of Statistics, University of Baghdad, Iraq
Abstract
The application of structural reliability analysis has become very important to ensure the strength of the studied structural design, as it presents results that help in giving evidence about the acceptance of that design according to the materials used under specific operating conditions. In this research an experiment was done, to find out the effect of G.U.M mouthwash on cured and re-cured Visible Light Cured (VLC) composite dental filling material, made according to agreed international standards, where many studies have documented that the surface of restorative materials placed on the tooth may also be affected by the chemical effect of different types of oral health care products, and the experiment was analyzed mathematically by applying structural reliability analysis to know the probability of structural failure when dental filling were exposed to the mouthwash G.U.M (Operational conditions), using analysis technique: the D-vine copula. The results were that the probability of structural failure gave an indication from which to infer the extent to which the experiment was accepted or rejected.
Keywords
[1] K. Aas, C. Czado, A. Frigessi and H. Bakken, Pair-copula constructions of multiple dependence, Insurance:
Mathematics and economics, 44 (2009) 182–98.
[2] S. Adhikari, Asymptotic distribution method for structural reliability analysis in high dimensions, Proceedings of
the Royal Society A: Mathematical, Physical and Engineering Sciences, 461 (2005) 3141–3158.
[3] T. Bedford and M. Cooke, Probability density decomposition for conditionally dependent random variables modeled
by Vines, Ann. Math. Artif. Intell., 32 (2001) 245–268.
[4] T. Bedford and M. Cooke, Vines–a new graphical model for dependent random variables, Ann. Stat., 30 (2002)
1031–1068.
[5] P. Cevik and A. Yildirim-bier, The effect of silica and prepolymer nanoparticles on the mechanical properties of
denture base acrylic resin, Journal of Prosthodontics, 27 (2016) 763-770.
[6] O. Ditlevsen and M Madsen, Structural reliability methods, Wiley, New york, 2007.
[7] Du, Juan and Li, Haibin and He, Yun, The method of solving structural reliability with multipara meter correlation
problem, Mathematical Problems in Engineering, 2017 (2017) 1–13.
[8] U. Erdemir, Surface hardness of different restorative materials after long-term immersion in sports and energy
drinks, Dental materials journal,31 (2012) 729-736.
[9] A. Hosni, E. Mesbahi and Y. Pu, Reliability analysis of structures using neural network method. Probabilistic
Engineering Mechanics, 21 (2006) 44-53.
[10] N. Ilie and R. Hickel, Resin composite restorative materials, Australian dental journal, 56 (2011) 59-66.
[11] C. Jiang, W. Zhang, X. Han, Y. Ni and J. Song, A Vine-copula-based reliability analysis method for structures
with multidimensional correlation, Journal of Mechanical Design, 137 (2015) 1–13.
[12] Ch. Jiang, Sh. Han, M. Ji and X. Han, A new method to solve the structural reliability index based on homology
analysis, 226 (2014) 1067–1083.
[13] H. Joe,Dependence modeling with copulas, Taylor & Francis Group, LLC. 2015.
[14] B. K. Keshtegar and Z. Meng, A hybrid relaxed first-order reliability method for efficient structural reliability
analysis, Structural Safety, 66 (2017) 84-93.
[15] B. Keshtegar and S. Chakraborty, An efficient -robust structural reliability method by adaptive finite-step length
based on Armijo line search, Reliability Engineering and System Safety, 172 (2018) 195–206.
[16] D. Kiureghian, M. ASCE and P.Liu, Structural reliability under incomplete probability information, Journal of
Engineering Mechanics, 112 (1986) 85-104.
[17] R. Kochhar, An evaluation and comparison of the effect of five mouthrinses on the microhardness of esthetic
hybrid composite restorative material-an in vitro study, Journal of Dental Specialities, 5 (2017) 66-69.
[18] D. Kurowicka and R. Cooke, Uncertainty analysis with high dimensional dependence modeling, John Wiley &
Sons Ltd. 2006.
[19] D. Kurowicka and H. Joe, Dependence modeling: Vine Copula Handbook, World Scientific Publishing Co. Pte.
Ltd. 2011.
[20] M. Lemaire, Structural Reliability, John Wiley & Sons, Inc. 2009.
[21] Q. Lia, Y. Caia, H. Wanga, Z. Lva and E. Lic, An efficient D-vine copula-based coupling uncertainty analysis for
variable stiffness composites, Composite Structures, 219 (2019) 221-241.
[22] B. Low and WH Tang, Efficient spreadsheet algorithm for first-order reliability method, Journal of engineering
mechanics, 133 (2007) 1378-87.
[23] T. Lüa, X. Tanga, D. Lia and X. Qid, Modeling multivariate distribution of multiple soil parameters using vine
copula model, Computers and Geotechnics, 118 (2020) 1-14.
[24] R. Melchers and A. Beck, Structural Reliability Analysis and Prediction, John Wiley & Sons Ltd. 2018.
[25] Z. Meng, G. Li, D. Yang and L. Zhan, A new directional stability transformation method of chaos control for first
order reliability analysis, Structural and Multidisciplinary Optimization, 55 (2017) 601–612.
[26] A. Min and C. Czado, Bayesian inference for multivariate copulas using pair-copula constructions, Journal of
Financial Econometrics, 8 (2010) 511–546.[27] R. Montes and E. Heredia, Assessment of uncertainty in environmental contours due to parametric uncertainty
in models of the dependence structure between metocean variables, Applied Ocean Research, 64 (2017) 86-104.
[28] B. Nelson, An introduction to copulas, Springer, Berlin, 2006.
[29] B. Nezhad, M. Miri and M. Ghasemi, New neural network-based response surface method for reliability analysis
of structures, Neural Computing and Applications, 31 (2017) 777–791.
[30] J. Nie and R. Ellingwood, Directional methods for structural reliability analysis, Structural Safety, 22 (200)
233-249.
[31] y. Noh, K. Choi and L. Du, New Transformation of Dependent Input Variables Using Copula for RBDO, 7th
World Congresses of Structural and Multidisciplinary Optimization, COEX Seoul, Korea, 2007.
[32] Y. Noh, K. Choi and L. Du, Reliability-based design optimization of problems with correlated input variables using
a Gaussian Copula, Struct Multidisc Optim, 38 (2009) 1–16.
[33] X. Ren, SH Li, CH. Lv and Z. Zhang, Sequential Dependence Modeling Using Bayesian Theory and D‑Vine Copula
and its Application on Chemical Process Risk Prediction, Ind. Eng. Chem. Res., 53 (2014) 14788–14801.
[34] A. Strauss, S. Hoffmann, R. Wendner and K. Bergmeister, Structural assessment and reliability analysis for
existing engineering structures applications for real structures, Structure and Infrastructure Engineering, 5 (2009)
277–286.
[35] Y. Sun, L. Luo, Q. Zhang and X. Qin, Reliability analysis of stochastic structure with multi-failure modes based
on mixed Copula, Engineering Failure Analysis, 105 (2019) 930-944.
[36] X. Tang, D. Li, CH. Zhou and L. Zhang, Bivariate distribution models using copulas for reliability analysis,
Journal of Risk and Reliability, 77 (2013) 499-512.
[37] P. Trivedi and D. Zimmer, Copula Modeling: An Introduction for Practitioners, Foundations and Trends in
Econometrics, now Publishers Inc. 2005.
[38] M. Valdebenito, H. Jensen, H. Hernandez and L. Mehrez, Sensitivity Estimation of Failure Probability Applying
Line Sampling, Reliability Engineering & System Safety, 1 (2017) 99-111.
[39] F. Wang, H. Li, Distribution modeling for reliability analysis: Impact of multiple dependences and probability
model selection, Applied Mathematical, 59 (2018) 483-499.
[40] F. Wang, H. Li, Towards reliability evaluation involving correlated multivariates under incomplete probability
information: A reconstructed joint probability distribution for isoprobabilistic transformation, Structural Safety,
69 (2017) 1-10.
[41] F. Wang, H. Li, Subset simulation for non-Gaussian dependent random variables given incomplete probability
information, Structural Safety, 67 (2017) 105–115.
[42] Z. Zhang, C. Jiang, GG. Wang and X. Han, First and second order approximate reliability analysis methods using
evidence theory, Reliability Engineering & System Safety, 137 (2015) 40–49.
[43] M. Zhang and M. Bedford, Vine copula approximation: a generic method for coping with conditional dependence,
Statistics and Computing, 28 (2016) 219–237.
[44] Y. Zhao and T. Ono, A general procedure first/second-order reliability method (FORM/SORM), Structural Safety,
21 (1999) 95-112.
[45] Ch. Zhong, M. Wang, Ch. Dang, W. Ke and and Sh. Guo, First-order reliability method based on Harris Hawks
Optimization for high-dimensional reliability analysis, Structural and Multidisciplinary Optimization, 62 (2020)
1951–1968 .
Mathematics and economics, 44 (2009) 182–98.
[2] S. Adhikari, Asymptotic distribution method for structural reliability analysis in high dimensions, Proceedings of
the Royal Society A: Mathematical, Physical and Engineering Sciences, 461 (2005) 3141–3158.
[3] T. Bedford and M. Cooke, Probability density decomposition for conditionally dependent random variables modeled
by Vines, Ann. Math. Artif. Intell., 32 (2001) 245–268.
[4] T. Bedford and M. Cooke, Vines–a new graphical model for dependent random variables, Ann. Stat., 30 (2002)
1031–1068.
[5] P. Cevik and A. Yildirim-bier, The effect of silica and prepolymer nanoparticles on the mechanical properties of
denture base acrylic resin, Journal of Prosthodontics, 27 (2016) 763-770.
[6] O. Ditlevsen and M Madsen, Structural reliability methods, Wiley, New york, 2007.
[7] Du, Juan and Li, Haibin and He, Yun, The method of solving structural reliability with multipara meter correlation
problem, Mathematical Problems in Engineering, 2017 (2017) 1–13.
[8] U. Erdemir, Surface hardness of different restorative materials after long-term immersion in sports and energy
drinks, Dental materials journal,31 (2012) 729-736.
[9] A. Hosni, E. Mesbahi and Y. Pu, Reliability analysis of structures using neural network method. Probabilistic
Engineering Mechanics, 21 (2006) 44-53.
[10] N. Ilie and R. Hickel, Resin composite restorative materials, Australian dental journal, 56 (2011) 59-66.
[11] C. Jiang, W. Zhang, X. Han, Y. Ni and J. Song, A Vine-copula-based reliability analysis method for structures
with multidimensional correlation, Journal of Mechanical Design, 137 (2015) 1–13.
[12] Ch. Jiang, Sh. Han, M. Ji and X. Han, A new method to solve the structural reliability index based on homology
analysis, 226 (2014) 1067–1083.
[13] H. Joe,Dependence modeling with copulas, Taylor & Francis Group, LLC. 2015.
[14] B. K. Keshtegar and Z. Meng, A hybrid relaxed first-order reliability method for efficient structural reliability
analysis, Structural Safety, 66 (2017) 84-93.
[15] B. Keshtegar and S. Chakraborty, An efficient -robust structural reliability method by adaptive finite-step length
based on Armijo line search, Reliability Engineering and System Safety, 172 (2018) 195–206.
[16] D. Kiureghian, M. ASCE and P.Liu, Structural reliability under incomplete probability information, Journal of
Engineering Mechanics, 112 (1986) 85-104.
[17] R. Kochhar, An evaluation and comparison of the effect of five mouthrinses on the microhardness of esthetic
hybrid composite restorative material-an in vitro study, Journal of Dental Specialities, 5 (2017) 66-69.
[18] D. Kurowicka and R. Cooke, Uncertainty analysis with high dimensional dependence modeling, John Wiley &
Sons Ltd. 2006.
[19] D. Kurowicka and H. Joe, Dependence modeling: Vine Copula Handbook, World Scientific Publishing Co. Pte.
Ltd. 2011.
[20] M. Lemaire, Structural Reliability, John Wiley & Sons, Inc. 2009.
[21] Q. Lia, Y. Caia, H. Wanga, Z. Lva and E. Lic, An efficient D-vine copula-based coupling uncertainty analysis for
variable stiffness composites, Composite Structures, 219 (2019) 221-241.
[22] B. Low and WH Tang, Efficient spreadsheet algorithm for first-order reliability method, Journal of engineering
mechanics, 133 (2007) 1378-87.
[23] T. Lüa, X. Tanga, D. Lia and X. Qid, Modeling multivariate distribution of multiple soil parameters using vine
copula model, Computers and Geotechnics, 118 (2020) 1-14.
[24] R. Melchers and A. Beck, Structural Reliability Analysis and Prediction, John Wiley & Sons Ltd. 2018.
[25] Z. Meng, G. Li, D. Yang and L. Zhan, A new directional stability transformation method of chaos control for first
order reliability analysis, Structural and Multidisciplinary Optimization, 55 (2017) 601–612.
[26] A. Min and C. Czado, Bayesian inference for multivariate copulas using pair-copula constructions, Journal of
Financial Econometrics, 8 (2010) 511–546.[27] R. Montes and E. Heredia, Assessment of uncertainty in environmental contours due to parametric uncertainty
in models of the dependence structure between metocean variables, Applied Ocean Research, 64 (2017) 86-104.
[28] B. Nelson, An introduction to copulas, Springer, Berlin, 2006.
[29] B. Nezhad, M. Miri and M. Ghasemi, New neural network-based response surface method for reliability analysis
of structures, Neural Computing and Applications, 31 (2017) 777–791.
[30] J. Nie and R. Ellingwood, Directional methods for structural reliability analysis, Structural Safety, 22 (200)
233-249.
[31] y. Noh, K. Choi and L. Du, New Transformation of Dependent Input Variables Using Copula for RBDO, 7th
World Congresses of Structural and Multidisciplinary Optimization, COEX Seoul, Korea, 2007.
[32] Y. Noh, K. Choi and L. Du, Reliability-based design optimization of problems with correlated input variables using
a Gaussian Copula, Struct Multidisc Optim, 38 (2009) 1–16.
[33] X. Ren, SH Li, CH. Lv and Z. Zhang, Sequential Dependence Modeling Using Bayesian Theory and D‑Vine Copula
and its Application on Chemical Process Risk Prediction, Ind. Eng. Chem. Res., 53 (2014) 14788–14801.
[34] A. Strauss, S. Hoffmann, R. Wendner and K. Bergmeister, Structural assessment and reliability analysis for
existing engineering structures applications for real structures, Structure and Infrastructure Engineering, 5 (2009)
277–286.
[35] Y. Sun, L. Luo, Q. Zhang and X. Qin, Reliability analysis of stochastic structure with multi-failure modes based
on mixed Copula, Engineering Failure Analysis, 105 (2019) 930-944.
[36] X. Tang, D. Li, CH. Zhou and L. Zhang, Bivariate distribution models using copulas for reliability analysis,
Journal of Risk and Reliability, 77 (2013) 499-512.
[37] P. Trivedi and D. Zimmer, Copula Modeling: An Introduction for Practitioners, Foundations and Trends in
Econometrics, now Publishers Inc. 2005.
[38] M. Valdebenito, H. Jensen, H. Hernandez and L. Mehrez, Sensitivity Estimation of Failure Probability Applying
Line Sampling, Reliability Engineering & System Safety, 1 (2017) 99-111.
[39] F. Wang, H. Li, Distribution modeling for reliability analysis: Impact of multiple dependences and probability
model selection, Applied Mathematical, 59 (2018) 483-499.
[40] F. Wang, H. Li, Towards reliability evaluation involving correlated multivariates under incomplete probability
information: A reconstructed joint probability distribution for isoprobabilistic transformation, Structural Safety,
69 (2017) 1-10.
[41] F. Wang, H. Li, Subset simulation for non-Gaussian dependent random variables given incomplete probability
information, Structural Safety, 67 (2017) 105–115.
[42] Z. Zhang, C. Jiang, GG. Wang and X. Han, First and second order approximate reliability analysis methods using
evidence theory, Reliability Engineering & System Safety, 137 (2015) 40–49.
[43] M. Zhang and M. Bedford, Vine copula approximation: a generic method for coping with conditional dependence,
Statistics and Computing, 28 (2016) 219–237.
[44] Y. Zhao and T. Ono, A general procedure first/second-order reliability method (FORM/SORM), Structural Safety,
21 (1999) 95-112.
[45] Ch. Zhong, M. Wang, Ch. Dang, W. Ke and and Sh. Guo, First-order reliability method based on Harris Hawks
Optimization for high-dimensional reliability analysis, Structural and Multidisciplinary Optimization, 62 (2020)
1951–1968 .
)
Volume 12, Issue 2
November 2021Pages 2555-2569
- Receive Date: 11 March 2021
- Revise Date: 28 April 2021
- Accept Date: 20 May 2021