An Envelope Approach to Time-Dependent Reliability Analysis for Mechanisms

2013 ◽  
Author(s):  
Xiaoping Du
Keyword(s):  
Reliability Analysis ◽  
Envelope Function ◽  
Time Dependent ◽  
Normal Distribution Function ◽  
Maximum Probability ◽  
Accuracy Improvement ◽  
Motion Error ◽  
Time Period ◽  
Time Dependent Problem ◽  
Dependent Mechanism

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.

Time-Dependent Mechanism Reliability Analysis With Envelope Functions and First-Order Approximation

2014 ◽  
Vol 136 (8) ◽  
Author(s):  
Xiaoping Du
Keyword(s):  
Order Approximation ◽  
Envelope Function ◽  
Time Dependent ◽  
Maximum Probability ◽  
Accuracy Improvement ◽  
Motion Error ◽  
First Order ◽  
First Order Approximation ◽  
Dependent Mechanism ◽  
Envelope Functions

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.

scholarly journals Time-dependent Reliability Analysis of Timber-Concrete Composite Beams

2017 ◽  
Author(s):  
Nikola Velimirovic ◽  
Dragoslav Stojić ◽  
Miodrag Djordjević ◽  
Gordana Topličić-Ćurčić
Keyword(s):  
Reliability Analysis ◽  
Process Model ◽  
Composite System ◽  
Random Variable ◽  
Composite Beams ◽  
Time Dependent ◽  
Deterioration Rate ◽  
Time Period ◽  
Deterioration Process ◽  
Service Life Estimation

Timber-concrete composite system is increasing the use of timber in construction because some structures could not be built by timber alone, but it becomes possible with this composite system. The deterioration of structures in service is generally uncertain over time, therefore the appropriate approach for the structural analysis is a time-dependent reliability analysis that considers the randomness and uncertainties of deterioration process over a time period. This paper describes two methods for time dependent reliability analysis, random variable deterioration rate model and gamma process model, and compares the deterioration prediction as well as service life estimation of timber-concrete composite beams under normal use based on proposed models.

Time-Dependent Reliability Analysis for Function Generator Mechanisms

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Junfu Zhang ◽  
Xiaoping Du
Keyword(s):  
Gaussian Process ◽  
Reliability Analysis ◽  
Functional Relationship ◽  
Numerical Procedure ◽  
Mean Value ◽  
Time Dependent ◽  
Time Interval ◽  
First Passage ◽  
Function Generator ◽  
Motion Error

A function generator mechanism links its motion output and motion input with a desired functional relationship. The probability of realizing such functional relationship is the kinematic reliability. The time-dependent kinematic reliability is desired because it provides the reliability over the time interval where the functional relationship is defined. But the methodologies of time-dependent reliability are currently lacking for function generator mechanisms. We propose a mean value first-passage method for time-dependent reliability analysis. With the assumption of normality for random dimension variables with small variances, the motion error becomes a nonstationary Gaussian process. We at first derive analytical equations for upcrossing and downcrossing rates and then develop a numerical procedure that integrates the two rates to obtain the kinematic reliability. A four-bar function generator is used as an example. The proposed method is accurate and efficient for normally distributed dimension variables with small variances.

scholarly journals Time-Dependent Reliability Analysis of Reinforced Concrete Beams Subjected to Uniform and Pitting Corrosion and Brittle Fracture

Materials ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 1820
Author(s):  
Mohamed El Amine Ben Seghier ◽  
Behrooz Keshtegar ◽  
Hussam Mahmoud
Keyword(s):  
Reinforced Concrete ◽  
Brittle Fracture ◽  
Reliability Analysis ◽  
Pitting Corrosion ◽  
Structural Reliability ◽  
Time Dependent ◽  
State Function ◽  
Rc Beams ◽  
Highly Nonlinear ◽  
Reliability Method

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.

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