Reliability Analysis of Underground Structures Using Metamodels and FORM

2019 ◽  
Author(s):  
Qian Wang ◽  
Jun Ji
Keyword(s):  
Reliability Analysis ◽  
Alternative Form ◽  
Underground Structures ◽  
Mathematical Functions ◽  
Performance Function ◽  
Reliability Indices ◽  
Nonlinear Responses ◽  
Reliability Method ◽  
Practical Engineering ◽  
Implicit Response

<p>An engineering reliability analysis method of underground structures using metamodels and a first-order reliability method (FORM) was studied. Surrogate models, or metamodels are approximate models that can be constructed to replace implicit response functions that involve finite element analyses. The radial basis functions (RBFs) are suitable for creating metamodels for general linear or nonlinear responses and they are locally and globally adaptive. After a performance function was replaced by an augmented RBF metamodel, an alternative FORM was applied. The method was tested using mathematical functions and applied to a tunnel engineering example. Different numbers of samples were tested and reliability analyses were performed. The failure probabilities and reliability indices were found to have a good accuracy. The proposed method combining RBFs and FORM is useful for practical engineering problems involving expensive response simulations.</p>

AN ITERATIVE HDMR APPROACH FOR ENGINEERING RELIABILITY ANALYSIS

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Qian Wang
Keyword(s):  
Reliability Analysis ◽  
Probabilistic Analysis ◽  
Surrogate Models ◽  
Second Order ◽  
High Dimensional Model Representation ◽  
Performance Function ◽  
Reliability Indices ◽  
Reliability Method ◽  
Sample Points ◽  
A Performance

Engineering reliability analysis has long been an active research area. Surrogate models, or metamodels, are approximate models that can be created to replace implicit performance functions in the probabilistic analysis of engineering systems. Traditional 1st-order or second-order high dimensional model representation (HDMR) methods are shown to construct accurate surrogate models of response functions in an engineering reliability analysis. Although very efficient and easy to implement, 1st-order HDMR models may not be accurate, since the cross-effects of variables are neglected. Second-order HDMR models are more accurate; however they are more complicated to implement. Moreover, they require much more sample points, i.e., finite element (FE) simulations, if FE analyses are employed to compute values of a performance function. In this work, a new probabilistic analysis approach combining iterative HDMR and a first-order reliability method (FORM) is investigated. Once a performance function is replaced by a 1st-order HDMR model, an alternate FORM is applied. In order to include higher-order contributions, additional sample points are generated and HDMR models are updated, before FORM is reapplied. The analysis iteration continues until the reliability index converges. The novelty of the proposed iterative strategy is that it greatly improves the efficiency of the numerical algorithm. As numerical examples, two engineering problems are studied and reliability analyses are performed. Reliability indices are obtained within a few iterations, and they are found to have a good accuracy. The proposed method using iterative HDMR and FORM provides a useful tool for practical engineering applications.

AN ENGINEERING RELIABILITY ANALYSIS METHOD BASED ON ADAPTIVE METAMODELS

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Qian Wang ◽  
Erica Jarosch ◽  
Hongbing Fang
Keyword(s):  
Reliability Analysis ◽  
Fe Method ◽  
Performance Function ◽  
Design Point ◽  
Reliability Method ◽  
Engineering Problems ◽  
Practical Engineering ◽  
Metamodeling Technique ◽  
Gradient Based ◽  
Adaptive Metamodeling

In practical engineering problems, numerical analyses using the finite element (FE) method or other methods are generally required to evaluate system responses including stresses and deformations. For problems involving expensive FE analyses, it is not efficient or straightforward to directly apply conventional sampling-based or gradient-based reliability analysis approaches. To reduce computational efforts, it is useful to develop efficient and accurate metamodeling techniques to replace the original FE analyses. In this work, an adaptive metamodeling technique and a First-Order Reliability Method (FORM) were integrated. In each adaptive iteration, a compactly supported radial basis function (RBF) was adopted and a metamodel was created to explicitly express a performance function. An alternate FORM was implemented to calculate reliability index of the current iteration. Based on the design point, additional samples were generated and added to the existing sample points to re-generate the metamodel. The accuracy of the RBF metamodel could be improved in the neighborhood of the design point at each iteration. This procedure continued until the convergence of the reliability analysis results was achieved. A numerical example was studied. The proposed adaptive approach worked well and reliability analysis results were found with a reasonable number of iterations.

A SEQUENTIAL AUGMENTED METAMODELING METHOD FOR ENGINEERING RELIABILITY ANALYSIS

2020 ◽  
Vol 7 (1) ◽  
Author(s):  
Qian Wang ◽  
Jun Ji
Keyword(s):  
Sample Size ◽  
Reliability Analysis ◽  
Limit State ◽  
Engineering Systems ◽  
Analysis Method ◽  
Model Accuracy ◽  
Performance Function ◽  
Analysis And Design ◽  
Optimal Sample ◽  
Practical Engineering

Metamodeling methods provide useful tools to replace expensive numerical simulations in engineering reliability analysis and design optimization. The radial basis functions (RBFs) and augmented RBFs can be used to create accurate metamodels; therefore they can be integrated with a reliability analysis method such as the Monte Carlo simulations (MCS). However the model accuracy of RBFs depends on the sample size, and the accuracy generally increases as the sample size increases. Since the optimal sample size used to create RBF metamodels is not known before the creation of the models, a sequential RBF metamodeling method was studied. In each iteration of reliability analysis, augmented RBFs were used to generate metamodels of a limit state or performance function, and the failure probability was calculated using MCS. Additional samples were generated in subsequent analysis iterations in order to improve the metamodel accuracy. Numerical examples from literature were solved, and the failure probabilities based on the RBF metamodels were found to have a good accuracy. In addition, only small numbers of iterations were required for the reliability analysis to converge. The proposed method based on sequential RBF metamodels is useful for probabilistic analysis of practical engineering systems.

Assessment of time-dependent reliability of reinforced concrete columns with uncertain load eccentricity

2000 ◽  
Vol 27 (3) ◽  
pp. 389-399
Author(s):  
H P Hong ◽  
W Zhou
Keyword(s):  
Reinforced Concrete ◽  
Reliability Analysis ◽  
Axial Load ◽  
Bending Moment ◽  
Time Dependent ◽  
Sensitivity Analyses ◽  
Live Load ◽  
Rc Columns ◽  
Reliability Indices ◽  
Reliability Method

An approach for the time-dependent reliability analysis of reinforced concrete (RC) columns considering the correlation between the axial load and the bending moment or the uncertainty in the load eccentricity is presented. The approach recursively uses the efficient first-order reliability method for the time-dependent reliability analysis. The proposed approach is more efficient than the ones used in the literature for the reliability analysis of RC columns. The proposed approach is used to carry out sensitivity analyses of the reliability of short RC columns to the time-dependent live load effects and to the correlation between the axial load and the bending moment. Results of the analyses suggest that the reliability of RC columns can be sensitive to the correlation between the axial load and the bending moment due to live load. The differences between the reliability indices obtained by considering the live load modeled as a pulse process and as an extreme variate can be large.Key words: reliability, load, time-dependent, time-independent, uncertainty, correlation, concrete, reinforcement, column.

Reliability Analysis of Subgrade Bearing Capacity of Gravity Foundation of Wind Turbine Based on JC Method

2011 ◽  
Vol 413 ◽  
pp. 314-319
Author(s):  
Zhong Qing Cheng ◽  
Ping Yang ◽  
Hai Bo Jiang
Keyword(s):  
Bearing Capacity ◽  
Wind Turbine ◽  
Reliability Analysis ◽  
Reliability Index ◽  
Maximum Pressure ◽  
Performance Function ◽  
Iterative Calculation ◽  
Reliability Method ◽  
Foundation Base ◽  
Index Effect

The design of foundation of wind turbine should meet the requirement of subgrade bearing capacity. In this paper, reliability method was used to analyze the bearing capacity of gravity foundation of wind turbine. The circular gravity foundation in coral sands is taken as research object. By deriving the expression of maximum pressure at the edge of foundation base under the action of overturning moment, the performance function of subgrade bearing capacity reliability analysis is established. JC method is used to calculate the subgrade bearing capacity reliability index. Effect of foundation size to reliability index is analyzed. Iterative calculation shows that the method proposed in this paper can calculate the reliability index of foundation quickly.

scholarly journals Reliability Analysis of a Solid Timber Column Subjected to Axial and Lateral Loading

2019 ◽  
Vol 4 (2) ◽  
Author(s):  
Sule Samuel ◽  
M J Benu
Keyword(s):  
Reliability Analysis ◽  
Failure Modes ◽  
Slenderness Ratio ◽  
Load Ratio ◽  
Failure Criteria ◽  
Lateral Loading ◽  
Reliability Indices ◽  
Reliability Method ◽  
Timber Column ◽  
Bending Failure

In this paper, a reliability analysis of a solid timber column of square cross section subjected to axial and lateral loading in accordance with the design requirements of Eurocode 5 is carried out. Compression and bending were the two failure criteria considered in the reliability investigation. The First Order Reliability method was employed to solve the limit state functions formed from the two failure criteria and was coded in MATLAB for quick estimation of the reliability indices. The results obtained showed that both the load and slenderness ratios have effects on the reliability of a solid timber column. The results of the sensitivity analysis carried out on the stochastic variables showed that the reliability indices decreased with increase in slenderness ratio for 3m, 4m and 5m length of column considering both the compression and bending failure modes and decreased with increase in load ratio for 3m, 4m and 5m length of column considering both the compression and bending failure modes. The reliability indices also decreased with increase in length of column mode and decreased with increase in ratio considering bending failure mode. The reliability indices were also found to decrease with increase in load ratio for varying values of axial and lateral loads at constant slenderness ratio and length of column considering compression and bending failure modes. The choice of adequate and suitable dimensions having a lower slenderness ratio will enhance the reliability of the column. Keywords- Reliability analysis, solid timber column, Eurocode 5, failure criteria, slenderness ratio 

Reliability Analysis and Design Considering Disjointed Active Failure Regions

2015 ◽  
Author(s):  
Pingfeng Wang ◽  
Xiaolong Cui ◽  
Zequn Wang
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Reliability Analysis ◽  
Failure Modes ◽  
Kriging Model ◽  
Engineering Systems ◽  
Random Input ◽  
Performance Function ◽  
Analysis And Design ◽  
Practical Engineering

Failure of practical engineering systems could be induced by several correlated failure modes, and consequently reliability analysis are conducted with multiple disjointed failure regions in the system random input space. Problems with disjointed failure regions create a great challenge for existing reliability analysis approaches due to the discontinuity of the system performance function between these regions. This paper presents a new enhanced Monte Carlo simulation (EMCS) approach for reliability analysis and design considering disjointed failure regions. The ordinary Kriging method is adopted to construct surrogate model for the performance function so that Monte Carlo simulation (MCS) can be used to estimate the reliability. A maximum failure potential based sampling scheme is developed to iteratively search failure samples and update the Kriging model. Two case studies are used to demonstrate the efficacy of the proposed methodology.

Reliability Analysis and Design Considering Disjointed Active Failure Regions

2015 ◽  
Author(s):  
Pingfeng Wang ◽  
Xiaolong Cui
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Reliability Analysis ◽  
Failure Modes ◽  
Kriging Model ◽  
Engineering Systems ◽  
Random Input ◽  
Performance Function ◽  
Analysis And Design ◽  
Practical Engineering

Failure of practical engineering systems could be induced by several correlated failure modes, and consequently reliability analysis are conducted with multiple disjointed failure regions in the system random input space. Problems with disjointed failure regions create a great challenge for existing reliability analysis approaches due to the discontinuity of the system performance function between these regions. This paper presents a new enhanced Monte Carlo simulation (EMCS) approach for reliability analysis and design considering disjointed failure regions. The ordinary Kriging method is adopted to construct surrogate model for the performance function so that Monte Carlo simulation (MCS) can be used to estimate the reliability. A maximum failure potential based sampling scheme is developed to iteratively search failure samples and update the Kriging model. Two case studies are used to demonstrate the efficacy of the proposed methodology.

Time-Dependent Reliability Analysis Through Response Surface Method

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Dequan Zhang ◽  
Xu Han ◽  
Chao Jiang ◽  
Jie Liu ◽  
Qing Li
Keyword(s):  
Reliability Analysis ◽  
Response Surface ◽  
Structural Reliability ◽  
Time Dependent ◽  
Gaussian Stochastic Process ◽  
Reliability Indices ◽  
Novel Approach ◽  
Reliability Method ◽  
Optimal Linear ◽  
Uncertain Structures

In time-dependent reliability analysis, the first-passage method has been extensively used to evaluate structural reliability under time-variant service circumstances. To avoid computing the outcrossing rate in this method, surrogate modeling may provide an effective alternative for calculating the time-dependent reliability indices in structural analysis. A novel approach, namely time-dependent reliability analysis with response surface (TRARS), is thus introduced in this paper to estimate the time-dependent reliability for nondeterministic structures under stochastic loads. A Gaussian stochastic process is generated by using the expansion optimal linear estimation (EOLE) method which has proven to be more accurate and efficient than some series expansion discretization techniques. The random variables and maximum responses of uncertain structures are treated as the input and output parameters, respectively. Through introducing the response surface (RS) model, a novel iterative procedure is proposed in this study. A Bucher strategy is adopted to generate the initial sample points, and a gradient projection technique is used to generate new sampling points for updating the RS model in each iteration. The time-dependent reliability indices and probabilities of failure are thus obtained efficiently using the first-order reliability method (FORM) over a certain design lifetime. In this study, four demonstrative examples are provided for illustrating the accuracy and efficiency of the proposed method.

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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