Reliability and reliability-based sensitivity analysis of self-centering buckling restrained braces using meta-models

2021 ◽  
pp. 1045389X2110263
Author(s):  
Seyede Vahide Hashemi ◽  
Mahmoud Miri ◽  
Mohsen Rashki ◽  
Sadegh Etedali
Keyword(s):  
Failure Probability ◽  
Limit State ◽  
Computational Cost ◽  
Sensitivity Analyses ◽  
State Function ◽  
Reliability Indices ◽  
Buckling Restrained Brace ◽  
Polynomial Response Surface ◽  
Nonlinear Dynamic Analyses ◽  
High Computational Cost

This paper aims to carry out sensitivity analyses to study how the effect of each design variable on the performance of self-centering buckling restrained brace (SC-BRB) and the corresponding buckling restrained brace (BRB) without shape memory alloy (SMA) rods. Furthermore, the reliability analyses of BRB and SC-BRB are performed in this study. Considering the high computational cost of the simulation methods, three Meta-models including the Kriging, radial basis function (RBF), and polynomial response surface (PRSM) are utilized to construct the surrogate models. For this aim, the nonlinear dynamic analyses are conducted on both BRB and SC-BRB by using OpenSees software. The results showed that the SMA area, SMA length ratio, and BRB core area have the most effect on the failure probability of SC-BRB. It is concluded that Kriging-based Monte Carlo Simulation (MCS) gives the best performance to estimate the limit state function (LSF) of BRB and SC-BRB in the reliability analysis procedures. Considering the effects of changing the maximum cyclic loading on the failure probability computation and comparison of the failure probability for different LSFs, it is also found that the reliability indices of SC-BRB were always higher than the corresponding reliability indices determined for BRB which confirms the performance superiority of SC-BRB than BRB.

Improved Line Sampling Reliability Analysis Method and its Application

2007 ◽  
Vol 353-358 ◽  
pp. 1001-1004 ◽  
Author(s):  
Shu Fang Song ◽  
Zhen Zhou Lu
Keyword(s):  
Markov Chain ◽  
Reliability Analysis ◽  
Failure Probability ◽  
Low Cycle Fatigue ◽  
Limit State ◽  
Computational Cost ◽  
State Function ◽  
Line Sampling ◽  
Failure Region ◽  
Important Direction

For reliability analysis of implicit limit state function, an improved line sampling method is presented on the basis of sample simulation in failure region. In the presented method, Markov Chain is employed to simulate the samples located at failure region, and the important direction of line sampling is obtained from these simulated samples. Simultaneously, the simulated samples can be used as the samples for line sampling to evaluate the failure probability. Since the Markov Chain samples are recycled for both determination of the important direction and calculation of the failure probability, the computational cost of the line sampling is reduced greatly. The practical application in reliability analysis for low cycle fatigue life of an aeronautical engine turbine disc structure under 0-takeoff-0 cycle load shows that the presented method is rational and feasible.

scholarly journals Gaussian Process-Based Response Surface Method for Slope Reliability Analysis

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Bin Hu ◽  
Guo-shao Su ◽  
Jianqing Jiang ◽  
Yilong Xiao
Keyword(s):  
Gaussian Process ◽  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Failure Probability ◽  
Limit State ◽  
State Function ◽  
Limit State Function ◽  
Surface Method ◽  
Gp Model

A new response surface method (RSM) for slope reliability analysis was proposed based on Gaussian process (GP) machine learning technology. The method involves the approximation of limit state function by the trained GP model and estimation of failure probability using the first-order reliability method (FORM). A small amount of training samples were firstly built by the limited equilibrium method for training the GP model. Then, the implicit limit state function of slope was approximated by the trained GP model. Thus, the implicit limit state function and its derivatives for slope stability analysis were approximated by the GP model with the explicit formulation. Furthermore, an iterative algorithm was presented to improve the precision of approximation of the limit state function at the region near the design point which contributes significantly to the failure probability. Results of four case studies including one nonslope and three slope problems indicate that the proposed method is more efficient to achieve reasonable accuracy for slope reliability analysis than the traditional RSM.

An Efficient Reliability Analysis Method for Structures With Epistemic Uncertainty Using Evidence Theory

2014 ◽  
Author(s):  
Zhe Zhang ◽  
Chao Jiang ◽  
G. Gary Wang ◽  
Xu Han
Keyword(s):  
Reliability Analysis ◽  
Structural Reliability ◽  
Epistemic Uncertainty ◽  
Limit State ◽  
Computational Cost ◽  
Evidence Theory ◽  
State Function ◽  
Limited Information ◽  
Design Point ◽  
Engineering Problems

Evidence theory has a strong ability to deal with the epistemic uncertainty, based on which the uncertain parameters existing in many complex engineering problems with limited information can be conveniently treated. However, the heavy computational cost caused by its discrete property severely influences the practicability of evidence theory, which has become a main difficulty in structural reliability analysis using evidence theory. This paper aims to develop an efficient method to evaluate the reliability for structures with evidence variables, and hence improves the applicability of evidence theory for engineering problems. A non-probabilistic reliability index approach is introduced to obtain a design point on the limit-state surface. An assistant area is then constructed through the obtained design point, based on which a small number of focal elements can be picked out for extreme analysis instead of using all the elements. The vertex method is used for extreme analysis to obtain the minimum and maximum values of the limit-state function over a focal element. A reliability interval composed of the belief measure and the plausibility measure is finally obtained for the structure. Two numerical examples are investigated to demonstrate the effectiveness of the proposed method.

Calibration of Load and Resistance Factors for the Design of Cable Members in Cable-supported Bridges Using Optimization of Strength

2019 ◽  
Author(s):  
Ho Hyun Lee ◽  
Hae Sung Lee
Keyword(s):  
Limit State ◽  
Target Strength ◽  
State Function ◽  
Reliability Indices ◽  
Resistance Factors ◽  
Reliability Level ◽  
Code Calibration ◽  
Structural Types ◽  
Nominal Strength ◽  
Load And Resistance Factors

<p>This proceeding presents the calibration process of load and resistance factors for the design of cable members under a gravitational loads-governed limit state adopting optimization scheme. In reliability-based bridge design code, although the cable members show various behavior depending on the structural types of bridges, a proper reliability level should be satisfied by the load and resistance factors. A cable is a nonlinear component, thus tension of it also shows nonlinear characteristics. In this study, the limit state function is linearized, and the tension of each load component is normalized by total nominal tension. With the purpose of performing code calibration independent of structural types of bridges, the normalized tensions are parameterized by three load ratios. The target reliability indices of cable members are determined considering results of reliability analyses of existing cable-supported bridges in South Korea, and a target strength, which satisfies the target reliability indices exactly, is evaluated. Optimization problem to minimize an error between the target strength and nominal strength, which is calculated by the load and resistance factors, is defined, and optimal values of the factors are calibrated. Reliability analyses for the strength calculated from the optimal factors are performed and it is verified that the factors can lead to the design with a uniform reliability level.</p>

Reliability Analysis for Structures With Multiple Temporal and Spatial Parameters Based on the Effective First-Crossing Point

2017 ◽  
Vol 139 (12) ◽  
Author(s):  
Yan Shi ◽  
Zhenzhou Lu ◽  
Kaichao Zhang ◽  
Yuhao Wei
Keyword(s):  
Failure Probability ◽  
Limit State ◽  
Function Technique ◽  
State Function ◽  
Fourth Moment ◽  
Dynamic Failure ◽  
Dynamic Reliability ◽  
Spatial Parameters ◽  
Temporal And Spatial ◽  
Crossing Point

For efficiently estimating the dynamic failure probability of the structure with the multiple temporal and spatial parameters, a transferred limit state function technique is first proposed in this paper. By finding the effective first-crossing point which controls the failure of the structural system, the transferred technique is constructed to transform the dynamic reliability problem into a static one. For determining the effective first-crossing point, the parameter domain is first divided into different dominant domain corresponding to every parameter. Based on the parameter dominant domain, the first-crossing point about each parameter is obtained by comparing the difference value between the point on the failure boundary and the corresponding parameter upper bound. Finally, the effective first-crossing point is determined by finding the point which controls the structure failure. With the transferred technique, two strategies (including the sparse grid integration based on fourth-moment method and the maximum entropy based on dimensional reduction method) are proposed to efficiently estimate the dynamic failure probability. Several examples are employed to illustrate the significance and effectiveness of the transferred technique and the proposed methods for solving the multiple temporal and spatial parameters dynamic reliability. The results show that the proposed methods can estimate the multiple temporal and spatial parameters dynamic failure probability efficiently and accurately.

scholarly journals Predictable Behavior of GFRP-Reinforced Bridge Decks: Formulation of a Strain-Based Capacity Model

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Young Hoon Kim ◽  
Yeesock Kim ◽  
Yeonho Park
Keyword(s):  
Failure Modes ◽  
Limit State ◽  
State Function ◽  
Limit State Function ◽  
Analysis Framework ◽  
Multiple Failure Modes ◽  
Reliability Indices ◽  
Capacity Model ◽  
Exposure Temperature ◽  
Over Time

This paper proposes a reliability analysis framework for glass fiber-reinforced polymer- (GFRP-) reinforced concrete systems with uncertain capacities and demands over time. Unfortunately, there has been limited discussion or research done related to the potential change of failure modes over time. Therefore, a rational approach is needed to integrate multiple failure modes in a single analysis framework, considering uncertainties of time-variant demands and capacities. To account for multiple failure modes, this study proposes the limit state function to estimate the safety margin, based on strain values of GFRP-reinforcing bars. A proposed limit state function can capture the likelihood of both shear and flexural failure modes, simultaneously. In this study, seven typical bridge deck configurations (e.g., varied deck thickness, girder spacing, and bar size) were exposed to various ambient temperatures. Simulation results show that reliability indices of 100-year exposure exhibit significant variance, ranging from 2.35 to 0.93, with exposure temperatures ranging from 13 to 33°C. Exposure temperature and time are the dominant factors influencing the reliability indices, so are the ones that need to be changed. As exposure time and/or exposure temperature increase, the flexural capacity model plays an important role to determine the reliability indices. When flexural and shear failure modes are equally dominant, reliability indices can capture risks of both failures, using the proposed strain-based approach.

Time-Dependent Reliability of Dynamic Systems Using Subset Simulation With Splitting Over a Series of Correlated Time Intervals

2013 ◽  
Author(s):  
Zhonglai Wang ◽  
Zissimos P. Mourelatos ◽  
Jing Li ◽  
Amandeep Singh ◽  
Igor Baseski
Keyword(s):  
Stochastic Processes ◽  
Dynamic Systems ◽  
Failure Probability ◽  
Limit State ◽  
Computational Cost ◽  
Reliability Estimation ◽  
Time Dependent ◽  
Cumulative Distribution ◽  
High Dimensional ◽  
Subset Simulation

Time-dependent reliability is the probability that a system will perform its intended function successfully for a specified time. Unless many and often unrealistic assumptions are made, the accuracy and efficiency of time-dependent reliability estimation are major issues which may limit its practicality. Monte Carlo simulation (MCS) is accurate and easy to use but it is computationally prohibitive for high dimensional, long duration, time-dependent (dynamic) systems with a low failure probability. This work addresses systems with random parameters excited by stochastic processes. Their response is calculated by time integrating a set of differential equations at discrete times. The limit state functions are therefore, explicit in time and depend on time-invariant random variables and time-dependent stochastic processes. We present an improved subset simulation with splitting approach by partitioning the original high dimensional random process into a series of correlated, short duration, low dimensional random processes. Subset simulation reduces the computational cost by introducing appropriate intermediate failure sub-domains to express the low failure probability as a product of larger conditional failure probabilities. Splitting is an efficient sampling method to estimate the conditional probabilities. The proposed subset simulation with splitting not only estimates the time-dependent probability of failure at a given time but also estimates the cumulative distribution function up to that time with approximately the same cost. A vibration example involving a vehicle on a stochastic road demonstrates the advantages of the proposed approach.

Reliability Analysis Method Based on Support Vector Machines Classification and Adaptive Sampling Strategy

2012 ◽  
Vol 544 ◽  
pp. 212-217 ◽  
Author(s):  
Hong Yan Hao ◽  
Hao Bo Qiu ◽  
Zhen Zhong Chen ◽  
Hua Di Xiong
Keyword(s):  
Reliability Analysis ◽  
Adaptive Sampling ◽  
Limit State ◽  
Computational Cost ◽  
Sampling Strategy ◽  
Support Vector ◽  
State Function ◽  
Analysis Method ◽  
Design Problems ◽  
Vector Machines

For probabilistic design problems with implicit limit state functions encountered in practical application, it is difficult to perform reliability analysis due to the expensive computational cost. In this paper, a new reliability analysis method which applies support vector machine classification(SVM-C) and adaptive sampling strategy is proposed to improve the efficiency. The SVM-C constructs a model defining the boundary of failure regions which classifies samples as safe or failed using SVM-C, then this model is used to replace the true limit state function,thus reducing the computational cost. The adaptive sampling strategy is applied to select samples along the constraint boundaries. It can also improves the efficiency of the proposed method. In the end, a probability analysis example is presented to prove the feasible and efficient of the proposed method.

Sampling-Based RBDO Using Probabilistic Sensitivity Analysis and Virtual Support Vector Machine

2012 ◽  
Author(s):  
Hyeongjin Song ◽  
K. K. Choi ◽  
Ikjin Lee ◽  
Liang Zhao ◽  
David Lamb
Keyword(s):  
Sensitivity Analysis ◽  
Support Vector Machine ◽  
Probabilistic Sensitivity Analysis ◽  
Limit State ◽  
Computational Cost ◽  
Classification Method ◽  
Support Vector ◽  
State Function ◽  
Limit State Function ◽  
Virtual Samples

In this paper, a sampling-based RBDO method using a classification method is presented. The probabilistic sensitivity analysis is used to compute sensitivities of probabilistic constraints with respect to random variables. Since the probabilistic sensitivity analysis requires only the limit state function, and not the response surface or sensitivity of the response, an efficient classification method can be used for a sampling-based RBDO. The proposed virtual support vector machine (VSVM), which is a classification method, is a support vector machine (SVM) with virtual samples. By introducing virtual samples, VSVM overcomes the deficiency in existing SVM that uses only classification information as their input. In this paper, the universal Kriging method is used to obtain locations of virtual samples to improve the accuracy of the limit state function for highly nonlinear problems. A sequential sampling strategy effectively inserts new samples near the limit state function. In sampling-based RBDO, Monte Carlo simulation (MCS) is used for the reliability analysis and probabilistic sensitivity analysis. Since SVM is an explicit classification method, unlike implicit methods, computational cost for evaluating a large number of MCS samples can be significantly reduced. Several efficiency strategies, such as the hyper-spherical local window for generation of the limit state function and the Transformations/Gibbs sampling method to generate uniform samples in the hyper-sphere, are also applied. Examples show that the proposed sampling-based RBDO using VSVM yields better efficiency in terms of the number of required samples and the computational cost for evaluating MCS samples while maintaining accuracy similar to that of sampling-based RBDO using the implicit dynamic Kriging (D-Kriging) method.

Plastic hinges mechano-reliability analysis in the beams of RC frames structures

2020 ◽  
Vol 17 (5) ◽  
pp. 719-732
Author(s):  
Leyla Bouzid ◽  
Mohand Hamizi ◽  
Naceur-Eddine Hannachi ◽  
Aghiles Nekmouche ◽  
Karim Akkouche
Keyword(s):  
Compressive Strength ◽  
Yield Stress ◽  
Failure Probability ◽  
Limit State ◽  
State Function ◽  
Concrete Compressive Strength ◽  
Plastic Hinges ◽  
Content Type ◽  
Steel Bars ◽  
The Impact

Purpose The purpose of this study is to establish a relationship between causes and effects, the respect of materials characteristics values [concrete compressive strength (fc) and steel yield stress (fy)] and the norms of the construction dispositions value (covers). This study is motivated by the post-seismic damages related to the plastification of the reinforced concrete (RC)/beams sections, named plastic hinges. The results are given by fragility curves representing the failure probability (Pf) of the plastic hinges versus covers value. Design/methodology/approach A mechanical-reliability coupling methodology is proposed and performed on three frames (three, six and nine storey). For each frame, seven covers the value of reinforcement steel bars has been taken into account in the beams. After definition of the limit state function G(x), a process of idea to twin-track; deterministic and probabilistic, is considered. Thus, numerical simulations are carried out under ETABS© software, to extract a soliciting moments Ms(x). Then, ultimate moments Mu(x), the result of reliability approach are calculated using Monte Carlo Simulations. In this step, two random variables; concrete compressive strength in 28 days of age (fc) and steel yield stress (fy), have been studied. Findings In the mechanical study, the results show that, the first plastic hinge appears at the beams for all frames. In the reliability study, the (fy) variation shows that all plastic hinges are in failure domain, nevertheless, the (fc) variation leads to have all sections in the safety domain, except A7 and B7 models. The failure probability (Pf) calculation according to (fc) and (fy) shows that an absolute error of 0.5 cm in the steel bars covers can switch the frame from the safety domain to the failure domain. Originality/value The plastic hinges reliability of the RC/ frame structures is independent on the high of the structure. The (fc) random variable according to the used distribution law does not affect the reliability (safety or failure). However, the impact of the steel yield stress variation (fy) is not negligible. The errors in covers affect considerably the strength of the elements.

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