Time-dependent mechanism reliability analysis with imprecise probability distributions based on envelope function

Author(s):  
Zheng Zhang ◽  
Changcong Zhou ◽  
Qi Chang ◽  
Haihe Li ◽  
Zhufeng Yue
Author(s):  
Xiaoping Du

This work is concerned with the time-dependent mechanism reliability defined over a period of time where a certain motion output is required. An envelope approach is proposed to improve the accuracy of the time-dependent mechanism reliability analysis. The envelope function of the motion error over the time period is created. Since the envelope function is not explicitly related to time, the time-dependent problem is converted into a time-independent problem. Then the envelope function is approximated by piecewise hyper-planes. To find the expansion points of the hyper-planes, the approach linearizes the motion error at the means of random dimension variables, and this approximation is accurate because the tolerances or the variances of the dimension variables are small. Then the expansion points are found with the maximum probability density at the failure threshold. The time-dependent mechanism reliability is then estimated by a multivariable normal distribution function at the expansion points. As an example, analytical equations are derived for a four-bar function generating mechanism. The numerical example shows the significant accuracy improvement.


2014 ◽  
Vol 136 (8) ◽  
Author(s):  
Xiaoping Du

This work develops an envelope approach to time-dependent mechanism reliability defined in a period of time where a certain motion output is required. Since the envelope function of the motion error is not explicitly related to time, the time-dependent problem can be converted into a time-independent problem. The envelope function is approximated by piecewise hyperplanes. To find the expansion points for the hyperplanes, the approach linearizes the motion error at the means of random dimension variables, and this approximation is accurate because the tolerances of the dimension variables are small. The expansion points are found with the maximum probability density at the failure threshold. The time-dependent mechanism reliability is then estimated by a multivariable normal distribution at the expansion points. As an example, analytical equations are derived for a four-bar function generating mechanism. The numerical example shows the significant accuracy improvement.


Materials ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 1820
Author(s):  
Mohamed El Amine Ben Seghier ◽  
Behrooz Keshtegar ◽  
Hussam Mahmoud

Reinforced concrete (RC) beams are basic elements used in the construction of various structures and infrastructural systems. When exposed to harsh environmental conditions, the integrity of RC beams could be compromised as a result of various deterioration mechanisms. One of the most common deterioration mechanisms is the formation of different types of corrosion in the steel reinforcements of the beams, which could impact the overall reliability of the beam. Existing classical reliability analysis methods have shown unstable results when used for the assessment of highly nonlinear problems, such as corroded RC beams. To that end, the main purpose of this paper is to explore the use of a structural reliability method for the multi-state assessment of corroded RC beams. To do so, an improved reliability method, namely the three-term conjugate map (TCM) based on the first order reliability method (FORM), is used. The application of the TCM method to identify the multi-state failure of RC beams is validated against various well-known structural reliability-based FORM formulations. The limit state function (LSF) for corroded RC beams is formulated in accordance with two corrosion types, namely uniform and pitting corrosion, and with consideration of brittle fracture due to the pit-to-crack transition probability. The time-dependent reliability analyses conducted in this study are also used to assess the influence of various parameters on the resulting failure probability of the corroded beams. The results show that the nominal bar diameter, corrosion initiation rate, and the external loads have an important influence on the safety of these structures. In addition, the proposed method is shown to outperform other reliability-based FORM formulations in predicting the level of reliability in RC beams.


2020 ◽  
Vol 115 ◽  
pp. 104599 ◽  
Author(s):  
Mansour Bagheri ◽  
Seyed Abbas Hosseini ◽  
Behrooz Keshtegar ◽  
José A.F.O. Correia ◽  
Nguyen-Thoi Trung

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