Probability density evolution for time-varying reliability assessment of wing structures

    Sajad Saraygord Afshari   Affiliation
    ; Seid H. Pourtakdoust   Affiliation


Reliability evaluation is a key factor in serviceability and safety analysis of air vehicles. Structural health monitoring methods have grown to a degree of maturity in many industries. However, there is a challenging interest to tie in SHM with reliability assessment. In this respect, consideration of stochastic structural dynamics with SHM data and random loadings opens a new chapter in failure prevention. The current study focuses on the stochastic behavior of structures as a way to relate SHM data with reliability. In this respect, uncertain factors such as atmospheric turbulence, structural parameters, and sensor outputs are considered in the process of reliability assessment. Firstly, an experimental evaluation is conducted using a simple cantilevered beam. Subsequently, system identification is weaved in with a probability density evolution equation for calculating the reliability of a wing structural component. Numerical simulations demonstrate that structural reliability of a typical WSC can be effectively evaluated. The proposed scheme paves the way for new SHM research topics such as online life prediction and reliability based failure prevention.

Keyword : system identification, reliability assessment, stochastic loadings, online SHM, structural health monitoring, life rediction

How to Cite
Saraygord Afshari, S., & Pourtakdoust, S. H. (2018). Probability density evolution for time-varying reliability assessment of wing structures. Aviation, 22(2), 45-54.
Published in Issue
Oct 16, 2018
Abstract Views
PDF Downloads
Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.


Belisario-Briceno, A., Zedek, S., Camps, T., François, R., Escriba, C., & Fourniols, J. Y. (2014). SHM based on modal analysis: accelerometer and piezoelectric transducers instrumentation for civil engineering in heterogeneous structures. Paper presented at the EWSHM-7th European Workshop on Structural Health Monitoring.

Fassois, S. D., & Sakellariou, J. S. (2009). Statistical time series methods for SHM. Encyclopedia of Structural Health Monitoring. John Wiley & Sons, Ltd.

Grondel, S., Assaad, J., Delebarre, C., & Moulin, E. (2004). Health monitoring of a composite wingbox structure. Ultrasonics, 42(1), 819-824.

Hoblit, F. M. (1988). Gust loads on aircraft: concepts and applications. AIAA.

Hosseini Kordkheili, S., Salmani, H., & Afshari, S. (2016). A stabilized piezolaminated nine-nodded shell element formulation for analyzing smart structures behaviors. Mechanics of Advanced Materials and Structures, 23(2), 187-194.

Li, J. (2016). Probability density evolution method: background, significance and recent developments. Probabilistic Engineering Mechanics, 44, 111-117.

Li, J., & Chen, J. (2004). Probability density evolution method for dynamic response analysis of structures with uncertain parameters. Computational Mechanics, 34(5), 400-409.

Mustapha, F., Manson, G., Pierce, S., & Worden, K. (2005). Structural health monitoring of an annular component using a statistical approach. Strain, 41(3), 117-127.

Nobahari, H., Kordkheili, S. A. H., & Afshari, S. S. (2014). Hardware-in-the-loop optimization of an active vibration controller in a flexible beam structure using evolutionary algorithms. Journal of Intelligent Material Systems and Structures, 25(10), 1211-1223.

Okasha, N. M., Frangopol, D. M., Saydam, D., & Salvino, L. W. (2011). Reliability analysis and damage detection in high-speed naval craft based on structural health monitoring data. Structural Health Monitoring, 10(4), 361-379.

Qi, W., & Tian, S. (2013). Complex modal pseudo-excitation method for gust responses of wing structures. Paper presented at the Mechatronic Sciences, Electric Engineering and Computer (MEC), Proceedings 2013 International Conference on.

Raghavan, A., & Cesnik, C. E. (2007). Review of guided-wave structural health monitoring. Shock and Vibration Digest, 39(2), 91-116.

Raouf, N., & Pourtakdoust, S. H. (2017). Time-varying structural reliability of launch vehicle via extreme response approach. Journal of Spacecraft and Rockets, 54, 306-314.

Saraygord Afshari, S., & Pourtakdoust, S. H. (2017). Reliability-based optimization of an active vibration controller using evolutionary algorithms. Paper presented at the SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

Saraygord Afshari, S., & Pourtakdoust, S. H. (2018). Utility of probability density evolution method for experimental reliability‐based active vibration control. Structural Control and Health Monitoring, 25(8), e2199.

Soliman, M., Barone, G., & Frangopol, D. M. (2015). Fatigue reliability and service life prediction of aluminum naval ship details based on monitoring data. Structural Health Monitoring, 14(1), 3-19.

Trendafilova, I., Cartmell, M., & Ostachowicz, W. (2008). Vibration-based damage detection in an aircraft wing scaled model using principal component analysis and pattern recognition. Journal of Sound and Vibration, 313(3), 560-566.

Tuegel, E. J., Bell, R. P., Berens, A. P., Brussat, T., Cardinal, J. W., Gallagher, J. P., & Rudd, J. (2013). Aircraft structural reliability and risk analysis handbook (Vol. 1: Basic Analysis Methods). Retrieved from

Xu, Y., Zhang, J., Li, J., & Xia, Y. (2009). Experimental investigation on statistical moment-based structural damage detection method. Structural Health Monitoring, 8(6), 555-571.

Zhang, J., Xu, Y., Xia, Y., & Li, J. (2008). A new statistical moment-based structural damage detection method. Structural Engineering and Mechanics, 30(4), 445-466.

Zhang, J., Xu, Y. L., & Li, J. (2011). Integrated system identification and reliability evaluation of stochastic building structures. Probabilistic Engineering Mechanics, 26(4), 528-538.

Zhu, S. P., Huang, H. Z., Peng, W., Wang, H. K., & Mahadevan, S. (2016). Probabilistic Physics of Failure-based framework for fatigue life prediction of aircraft gas turbine discs under uncertainty. Reliability Engineering & System Safety, 146, 1-12.