Reliability Analysis of an Uncertain Single Degree of Freedom System Under Random Excitation


  • M. S. M. Noori Department of Civil Engineering, College of Engineering, University of Baghdad, Iraq
  • R. M. Abbas Department of Civil Engineering, College of Engineering, University of Baghdad, Iraq
Volume: 12 | Issue: 5 | Pages: 9252-9257 | October 2022 |


In practical engineering problems, uncertainty exists not only in external excitations but also in structural parameters. This study investigates the influence of structural geometry, elastic modulus, mass density, and section dimension uncertainty on the stochastic earthquake response of portal frames subjected to random ground motions. The North-South component of the El Centro earthquake in 1940 in California is selected as the ground excitation. Using the power spectral density function, the two-dimensional finite element model of the portal frame’s base motion is modified to account for random ground motions. A probabilistic study of the portal frame structure using stochastic finite elements utilizing Monte Carlo simulation is presented using the finite element program ABAQUS. The dynamic reliability and probability of failure of stochastic and deterministic structures based on the first-passage failure were examined and evaluated. The results revealed that the probability of failure increases due to the randomness of stiffness and mass of the structure. The influence of uncertain parameters on reliability analysis depends on the extent of variance in structural parameters.


Reliability, Monte Carlo simulation, uncertain system, random excitation, stochastic, finite element


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J. Li and S. Liao, "Response analysis of stochastic parameter structures under non-stationary random excitation," Computational Mechanics, vol. 27, no. 1, pp. 61–68, Jan. 2001. DOI:

J. Dai, W. Gao, N. Zhang, and N. Liu, "Seismic random vibration analysis of shear beams with random structural parameters," Journal of Mechanical Science and Technology, vol. 24, no. 2, pp. 497–504, Feb. 2010. DOI:

M. R. Machado, L. Khalij, and A. T. Fabro, "Dynamic Analysis of a Composite Structure under Random Excitation Based on the Spectral Element Method," International Journal of Nonlinear Sciences and Numerical Simulation, vol. 20, no. 2, pp. 179–190, Apr. 2019. DOI:

W. Gao and N. J. Kessissoglou, "Dynamic response analysis of stochastic truss structures under non-stationary random excitation using the random factor method," Computer Methods in Applied Mechanics and Engineering, vol. 196, no. 25, pp. 2765–2773, May 2007. DOI:

S. Adhikari and B. Pascual, "The ‘damping effect’ in the dynamic response of stochastic oscillators," Probabilistic Engineering Mechanics, vol. 44, pp. 2–17, Apr. 2016. DOI:

M. H. Soltani and S. H. Ghasemi, "Structural Drift Corresponding to the Critical Excitations," Journal of Structural Engineering and Geo-Techniques, vol. 10, no. 2, pp. 27–34, Dec. 2020.

K. Hacıefendioğlu, H. B. Başağa, and S. Banerjee, "Probabilistic analysis of historic masonry bridges to random ground motion by Monte Carlo Simulation using Response Surface Method," Construction and Building Materials, vol. 134, pp. 199–209, Mar. 2017. DOI:

K. Kiyoshi, "Semi-empirical Formula for the Seismic Characteristics of the Ground," Bulletin of the Earthquake Research Institute, University of Tokyo, vol. 35, no. 2, pp. 309–325, Sep. 1957.

H. Tajimi, "Statistical Method of Determining the Maximum Response of Building Structure During an Earthquake," Proceedings of the 2nd WCEE, vol. 2, pp. 781–798, 1960.

R. W. Clough and J. Penzien, Dynamics of Structures. New York: McGraw-Hill College, 1975.

S. P. Lai, "Statistical characterization of strong ground motions using power spectral density function," Bulletin of the Seismological Society of America, vol. 72, no. 1, pp. 259–274, Feb. 1982.

E. H. Vanmarcke, "Chapter 8 - Structural Response to Earthquakes," in Developments in Geotechnical Engineering, vol. 15, C. Lomnitz and E. Rosenblueth, Eds. Elsevier, 1976, pp. 287–337. DOI:

S. S. Kar and L. B. Roy, "Probabilistic Based Reliability Slope Stability Analysis Using FOSM, FORM, and MCS," Engineering, Technology & Applied Science Research, vol. 12, no. 2, pp. 8236–8240, Apr. 2022. DOI:

J. D. Arregui-Mena, L. Margetts, and P. M. Mummery, "Practical Application of the Stochastic Finite Element Method," Archives of Computational Methods in Engineering, vol. 23, no. 1, pp. 171–190, Mar. 2016. DOI:

D. T. Hang, X. T. Nguyen, and D. N. Tien, "Stochastic Buckling Analysis of Non-Uniform Columns Using Stochastic Finite Elements with Discretization Random Field by the Point Method," Engineering, Technology & Applied Science Research, vol. 12, no. 2, pp. 8458–8462, Apr. 2022. DOI:

Y. K. Wen and H.-C. Chen, "On fast integration for time variant structural reliability," Probabilistic Engineering Mechanics, vol. 2, no. 3, pp. 156–162, Sep. 1987. DOI:

W. T. Segui, Steel Design, 5th ed. Mason, OH, USA: Cengage Learning, 2013.

N. L. Tran and T. H. Nguyen, "Reliability Assessment of Steel Plane Frame’s Buckling Strength Considering Semi-rigid Connections," Engineering, Technology & Applied Science Research, vol. 10, no. 1, pp. 5099–5103, Feb. 2020. DOI:

"Abaqus Analysis User’s Guide (6.14)," Simulia.

Z. Kala, J. Melcher, and L. Puklicky, "Material and geometrical characteristics of structural steels based on statistical analysis of metallurgical products," Journal of Civil Engineering and Management, vol. 15, no. 3, pp. 299–308, Sep. 2009. DOI:

S. Zhang and W. Zhou, "System Reliability Assessment of 3d Steel Frames Designed Per AISC LRFD Specifications," Advanced Steel Construction, vol. 9, no. 1, pp. 77–89, 2016. DOI:

M. M. A. Moghaddam and M. Moudi, "Analysis of beam failure based on reliability system theory using monte carlo simulation method," in International Conference on Applied Computer Science - Proceedings, Jan. 2010, pp. 516–519.

A. S. Nowak and K. R. Collins, Reliability of Structures. New York, NY, USA: McGraw-Hill, 2000.

S. G. Buonopane and B. W. Schafer, "Reliability of Steel Frames Designed with Advanced Analysis," Journal of Structural Engineering, vol. 132, no. 2, pp. 267–276, Feb. 2006. DOI:


How to Cite

M. S. M. Noori and R. M. Abbas, “Reliability Analysis of an Uncertain Single Degree of Freedom System Under Random Excitation”, Eng. Technol. Appl. Sci. Res., vol. 12, no. 5, pp. 9252–9257, Oct. 2022.


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