Mixed Efficient Global Optimization for Time-Dependent Reliability Analysis

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Zhen Hu ◽  
Xiaoping Du
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Global Optimization ◽  
Reliability Analysis ◽  
Surrogate Model ◽  
Extreme Value ◽  
Time Dependent ◽  
Efficient Global Optimization ◽  
Highly Nonlinear ◽  
Adaptive Kriging

Time-dependent reliability analysis requires the use of the extreme value of a response. The extreme value function is usually highly nonlinear, and traditional reliability methods, such as the first order reliability method (FORM), may produce large errors. The solution to this problem is using a surrogate model of the extreme response. The objective of this work is to improve the efficiency of building such a surrogate model. A mixed efficient global optimization (m-EGO) method is proposed. Different from the current EGO method, which draws samples of random variables and time independently, the m-EGO method draws samples for the two types of samples simultaneously. The m-EGO method employs the adaptive Kriging–Monte Carlo simulation (AK–MCS) so that high accuracy is also achieved. Then, Monte Carlo simulation (MCS) is applied to calculate the time-dependent reliability based on the surrogate model. Good accuracy and efficiency of the m-EGO method are demonstrated by three examples.

Efficient Global Optimization Reliability Analysis (EGORA) for Time-Dependent Limit-State Functions

2014 ◽  
Author(s):  
Zhen Hu ◽  
Xiaoping Du
Keyword(s):  
Monte Carlo Simulation ◽  
Global Optimization ◽  
Surrogate Model ◽  
Limit State ◽  
Time Dependent ◽  
Efficient Global Optimization ◽  
State Function ◽  
Limit State Function ◽  
Extreme Response ◽  
Input Variables

If a limit-state function involves time, the associated reliability is defined within a period of time. The extreme value of the limit-state function is needed to calculate the time-dependent reliability, and the extreme value is usually highly nonlinear with respect to random input variables and may follow a multimodal distribution. For this reason, a surrogate model of the extreme response along with Monte Carlo simulation is usually employed. The objective of this work is to develop a new method, called the Efficient Global Optimization Reliability Analysis (EGORA), to efficiently build the surrogate model. EGORA is based on the Efficient Global Optimization (EGO) method. Different from the current method that generates training points for random variables and time independently, EGORA draws training points for the two types of input variables simultaneously and therefore accounts for their interaction effects. The other improvement is that EGORA only focuses on high accuracy at or near the limit state. With the two improvements, the new method can effectively reduce the number of training points. Once the surrogate model of the extreme response is available, Monte Carlo simulation is applied to calculate the time-dependent reliability. Good accuracy and efficiency of EGORA are demonstrated by three examples.

Reliability Analysis With Monte Carlo Simulation and Dependent Kriging Predictions

2016 ◽  
Vol 138 (12) ◽  
Author(s):  
Zhifu Zhu ◽  
Xiaoping Du
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Reliability Analysis ◽  
Surrogate Model ◽  
Limit State ◽  
Convergence Criterion ◽  
State Function ◽  
Kriging Method ◽  
Learning Function ◽  
Highly Nonlinear

Reliability analysis is time consuming, and high efficiency could be maintained through the integration of the Kriging method and Monte Carlo simulation (MCS). This Kriging-based MCS reduces the computational cost by building a surrogate model to replace the original limit-state function through MCS. The objective of this research is to further improve the efficiency of reliability analysis with a new strategy for building the surrogate model. The major approach used in this research is to refine (update) the surrogate model by accounting for the full information available from the Kriging method. The existing Kriging-based MCS uses only partial information. Higher efficiency is achieved by the following strategies: (1) a new formulation defined by the expectation of the probability of failure at all the MCS sample points, (2) the use of a new learning function to choose training points (TPs). The learning function accounts for dependencies between Kriging predictions at all the MCS samples, thereby resulting in more effective TPs, and (3) the employment of a new convergence criterion. The new method is suitable for highly nonlinear limit-state functions for which the traditional first- and second-order reliability methods (FORM and SORM) are not accurate. Its performance is compared with that of existing Kriging-based MCS method through five examples.

A New Reliability Analysis Method Combining Adaptive Kriging With Weight Index Monte Carlo Simulation

2018 ◽  
Vol 54 (3) ◽  
pp. 1-4 ◽  
Author(s):  
Jiangang Ma ◽  
Ziyan Ren ◽  
Guoxin Zhao ◽  
Yanli Zhang ◽  
Chang-Seop Koh
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Reliability Analysis ◽  
Analysis Method ◽  
Weight Index ◽  
Adaptive Kriging

scholarly journals Second Order Reliability Method for Time-Dependent Reliability Analysis Using Sequential Efficient Global Optimization

2019 ◽  
Author(s):  
Zhangli Hu ◽  
Xiaoping Du
Keyword(s):  
Global Optimization ◽  
Reliability Analysis ◽  
Limit State ◽  
Second Order ◽  
Time Dependent ◽  
Efficient Global Optimization ◽  
State Function ◽  
Limit State Function ◽  
Reliability Problem ◽  
Reliability Method

Abstract Reliability depends on time if the associated limit-state function includes time. A time-dependent reliability problem can be converted into a time-independent reliability problem by using the extreme value of the limit-state function. Then the first order reliability method can be used but it may produce a large error since the extreme limit-state function is usually highly nonlinear. This study proposes a new reliability method so that the second order reliability method can be applied to time-dependent reliability analysis for higher accuracy while maintaining high efficiency. The method employs sequential efficient global optimization to transform the time-dependent reliability analysis into the time-independent problem. The Hessian approximation and envelope theorem are used to obtain the second order information of the extreme limit-state function. Then the second order saddlepoint approximation is use to evaluate the reliability. The accuracy and efficiency of the proposed method are verified through numerical examples.

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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