Uncertainty Quantification of Time-Dependent Reliability Analysis in the Presence of Parametric Uncertainty

2016 ◽  
Vol 2 (3) ◽  
Author(s):  
Zhen Hu ◽  
Sankaran Mahadevan ◽  
Xiaoping Du
Keyword(s):  
Uncertainty Quantification ◽  
Reliability Analysis ◽  
Surrogate Model ◽  
Reliability Index ◽  
Integration Method ◽  
Epistemic Uncertainty ◽  
Random Variables ◽  
Time Dependent ◽  
Data Uncertainty ◽  
State Function

Limited data of stochastic load processes and system random variables result in uncertainty in the results of time-dependent reliability analysis. An uncertainty quantification (UQ) framework is developed in this paper for time-dependent reliability analysis in the presence of data uncertainty. The Bayesian approach is employed to model the epistemic uncertainty sources in random variables and stochastic processes. A straightforward formulation of UQ in time-dependent reliability analysis results in a double-loop implementation procedure, which is computationally expensive. This paper proposes an efficient method for the UQ of time-dependent reliability analysis by integrating the fast integration method and surrogate model method with time-dependent reliability analysis. A surrogate model is built first for the time-instantaneous conditional reliability index as a function of variables with imprecise parameters. For different realizations of the epistemic uncertainty, the associated time-instantaneous most probable points (MPPs) are then identified using the fast integration method based on the conditional reliability index surrogate without evaluating the original limit-state function. With the obtained time-instantaneous MPPs, uncertainty in the time-dependent reliability analysis is quantified. The effectiveness of the proposed method is demonstrated using a mathematical example and an engineering application example.

Uncertainty Quantification in Time-Dependent Reliability Analysis

2015 ◽  
Author(s):  
Zhen Hu ◽  
Sankaran Mahadevan ◽  
Xiaoping Du
Keyword(s):  
Uncertainty Quantification ◽  
Reliability Analysis ◽  
Surrogate Model ◽  
Reliability Index ◽  
Epistemic Uncertainty ◽  
Random Variables ◽  
Time Dependent ◽  
State Function ◽  
Uncertainty Sources ◽  
Stochastic Load

One of the essential steps in time-dependent reliability analysis is the characterization of stochastic load processes and system random variables based on experimental or historical data. Limited data results in uncertainty in the modeling of random variables and stochastic loadings. The uncertainty in random variable and stochastic load models later causes uncertainty in the results of reliability analysis. An uncertainty quantification framework is developed in this paper for time-dependent reliability analysis. The effects of two kinds of uncertainty sources, namely data uncertainty and model uncertainty on the results of time-dependent reliability analysis are investigated. The Bayesian approach is employed to model the epistemic uncertainty sources in random variables and stochastic processes. A straightforward formulation of uncertainty quantification in time-dependent reliability analysis results in a double-loop implementation, which is computationally expensive. Therefore, this paper builds a surrogate model for the conditional reliability index in terms of variables with imprecise parameters. Since the conditional reliability index is independent of the epistemic uncertainty, the surrogate model is applicable for any realizations of the epistemic uncertainty. Based on the surrogate model, the uncertainty in time-dependent reliability analysis is quantified without evaluating the original limit-state function, which increases the efficiency of uncertainty quantification. The effectiveness of the proposed method is demonstrated using a mathematical example and an engineering application example.

An LSTM-Based Ensemble Learning Approach for Time-Dependent Reliability Analysis

2020 ◽  
Vol 143 (3) ◽  
Author(s):  
Mingyang Li ◽  
Zequn Wang
Keyword(s):  
Reliability Analysis ◽  
Ensemble Learning ◽  
Short Term Memory ◽  
Limit State ◽  
Random Variables ◽  
Time Dependent ◽  
Independent Random Variables ◽  
State Function ◽  
Learning Approach ◽  
Lstm Network

Abstract This paper presents a long short-term memory (LSTM)-based ensemble learning approach for time-dependent reliability analysis. An LSTM network is first adopted to learn system dynamics for a specific setting with a fixed realization of time-independent random variables and stochastic processes. By randomly sampling the time-independent random variables, multiple LSTM networks can be trained and leveraged with the Gaussian process (GP) regression to construct a global surrogate model for the time-dependent limit state function. In detail, a set of augmented data is first generated by the LSTM networks and then utilized for GP modeling to estimate system responses under time-dependent uncertainties. With the GP models, the time-dependent system reliability can be approximated directly by sampling-based methods such as the Monte Carlo simulation (MCS). Three case studies are introduced to demonstrate the efficiency and accuracy of the proposed approach.

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.

scholarly journals Semi-Supervised Deep Learning for High-Dimensional Uncertainty Quantification

2020 ◽  
Author(s):  
Zequn Wang ◽  
Mingyang Li
Keyword(s):  
Uncertainty Quantification ◽  
Reliability Analysis ◽  
Supervised Learning ◽  
Dimensional Space ◽  
Limit State ◽  
Failure Surface ◽  
Simulation Method ◽  
High Dimensional ◽  
State Function ◽  
Latent Space

Abstract Conventional uncertainty quantification methods usually lacks the capability of dealing with high-dimensional problems due to the curse of dimensionality. This paper presents a semi-supervised learning framework for dimension reduction and reliability analysis. An autoencoder is first adopted for mapping the high-dimensional space into a low-dimensional latent space, which contains a distinguishable failure surface. Then a deep feedforward neural network (DFN) is utilized to learn the mapping relationship and reconstruct the latent space, while the Gaussian process (GP) modeling technique is used to build the surrogate model of the transformed limit state function. During the training process of the DFN, the discrepancy between the actual and reconstructed latent space is minimized through semi-supervised learning for ensuring the accuracy. Both labeled and unlabeled samples are utilized for defining the loss function of the DFN. Evolutionary algorithm is adopted to train the DFN, then the Monte Carlo simulation method is used for uncertainty quantification and reliability analysis based on the proposed framework. The effectiveness is demonstrated through a mathematical example.

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.

scholarly journals The Evaluation Of Algorithms For Determination Of The Reliability Index

2015 ◽  
Vol 61 (3) ◽  
pp. 133-147 ◽  
Author(s):  
A. Dudzik ◽  
U. Radoń
Keyword(s):  
Reliability Index ◽  
Limit State ◽  
Probabilistic Approach ◽  
Random Variables ◽  
Numerical Procedure ◽  
Vertical Displacement ◽  
Design Parameters ◽  
State Function ◽  
Structural Failure

AbstractThe study deals with stability and dynamic problems in bar structures using a probabilistic approach. Structural design parameters are defined as deterministic values and also as random variables, which are not correlated. The criterion of structural failure is expressed by the condition of non-exceeding the admissible load multiplier and condition of non-exceeding the admissible vertical displacement. The Hasofer-Lind index was used as a reliability measure. The primary research tool is the FORM method. In order to verify the correctness of the calculations Monte Carlo and Importance Sampling methods were used. The sensitivity of the reliability index to the random variables was defined. The limit state function is not an explicit function of random variables. This dependence was determined using a numerical procedure, e.g. the finite element methods. The paper aims to present the communication between the STAND reliability analysis program and the KRATA and MES3D external FE programs.

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.

Reliability Analysis of Nonlinear Vibratory Systems Under Non-Gaussian Loads Using a Sensitivity-Based Propagation of Moments

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Dimitrios Papadimitriou ◽  
Zissimos P. Mourelatos ◽  
Santosh Patil ◽  
Zhen Hu ◽  
Vasiliki Tsianika ◽  
...  
Keyword(s):  
Reliability Analysis ◽  
Autocorrelation Function ◽  
Computational Cost ◽  
Random Variables ◽  
Random Coefficients ◽  
Time Dependent ◽  
Vibratory System ◽  
First Order ◽  
Non Gaussian ◽  
First Four Moments

Abstract The paper proposes a new methodology for time-dependent reliability analysis of vibratory systems using a combination of a first-order, four-moment (FOFM) method and a non-Gaussian Karhunen–Loeve (NG-KL) expansion. The approach can also be used for random vibrations studies. The vibratory system is nonlinear and is excited by stationary non-Gaussian input random processes which are characterized by their first four marginal moments and autocorrelation function. The NG-KL expansion expresses each input non-Gaussian process as a linear combination of uncorrelated, non-Gaussian random variables and computes their first four moments. The FOFM method then uses the moments of the NG-KL variables to calculate the moments and autocorrelation function of the output processes based on a first-order Taylor expansion (linearization) of the system equations of motion. Using the output moments and autocorrelation function, another NG-KL expansion expresses the output processes in terms of uncorrelated non-Gaussian variables in the time domain, allowing the generation of output trajectories. The latter are used to estimate the time-dependent probability of failure using Monte Carlo simulation (MCS). The computational cost of the proposed approach is proportional to the number of NG-KL random variables and is significantly lower than that of other recently developed methodologies which are based on sampling. The accuracy and efficiency of the proposed methodology is demonstrated using a two-degree-of-freedom nonlinear vibratory system with random coefficients excited by a stationary non-Gaussian random process.

Reliability Analysis and Random Vibration of Nonlinear Systems Using the Adjoint Method and Projected Differentiation

2020 ◽  
Vol 143 (6) ◽  
Author(s):  
Dimitrios Papadimitriou ◽  
Zissimos P. Mourelatos ◽  
Zhen Hu
Keyword(s):  
Reliability Analysis ◽  
Equations Of Motion ◽  
Random Variables ◽  
Random Processes ◽  
Time Dependent ◽  
Vibratory System ◽  
Standard Normal ◽  
Non Gaussian ◽  
Nonlinear Equations Of Motion ◽  
Adjoint Approach

Abstract This paper proposes a new methodology for time-dependent reliability and random vibrations of nonlinear vibratory systems using a combination of a time-dependent adjoint variable (AV) method and a projected differentiation (PD) method. The proposed approach is called AV-PD. The vibratory system is excited by stationary Gaussian or non-Gaussian input random processes. A Karhunen–Loeve (KL) expansion expresses each input random process in terms of standard normal random variables. The nonlinear equations of motion (EOM) are linearized using a Taylor expansion using the first-order derivatives of the output with respect to the input KL random variables. An adjoint approach obtains the output derivatives accurately and efficiently requiring the solution of as many sets of EOM as the number of outputs of interest, independently of the number of KL random variables. The proposed PD method then computes the autocorrelation function of each output process at an additional cost of solving as many sets of EOM as the number of outputs of interest, independently of the time horizon (simulation time). A time-dependent reliability analysis is finally performed using a KL expansion of the output processes and Monte Carlo simulation (MCS). The number of solutions of the EOM scales only with the number of output random processes which is commonly much smaller than the number of input KL random variables. The efficiency and accuracy of the proposed approach is demonstrated using a four degree-of-freedom (DOF) half-car vibratory problem.

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