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.

Adaptive Virtual Support Vector Machine for the Reliability Analysis of High-Dimensional Problems

2011 ◽  
Author(s):  
Hyeongjin Song ◽  
K. K. Choi ◽  
Ikjin Lee ◽  
Liang Zhao ◽  
David Lamb
Keyword(s):  
Reliability Analysis ◽  
Limit State ◽  
Decision Function ◽  
High Dimensional ◽  
Support Vector ◽  
State Function ◽  
Limit State Function ◽  
Response Surface Methods ◽  
Virtual Samples ◽  
Virtual Support

In this study, an efficient classification methodology is developed for reliability analysis while maintaining the accuracy level similar to or better than existing response surface methods. The sampling-based reliability analysis requires only the classification information — a success or a failure – but the response surface methods provide real function values as their output, which requires more computational effort. The problem is even more challenging to deal with high-dimensional problems due to the curse of dimensionality. In the newly proposed virtual support vector machine (VSVM), virtual samples are generated near the limit state function by using linear or Kriging-based approximations. The exact function values are used for approximations of virtual samples to improve accuracy of the resulting VSVM decision function. By introducing the virtual samples, VSVM can overcome the deficiency in existing classification methods where only classified function values are used as their input. The universal Kriging method is used to obtain virtual samples to improve the accuracy of the decision function for highly nonlinear problems. A sequential sampling strategy that chooses a new sample near the true limit state function is integrated with VSVM to maximize the accuracy. Examples show the proposed adaptive VSVM yields better efficiency in terms of the modeling time and the number of required samples while maintaining similar level or better accuracy especially for high-dimensional problems.

High-Dimensional Reliability Analysis of Engineered Systems Involving Computationally Expensive Black-Box Simulations

2017 ◽  
Author(s):  
Mohammad Kazem Sadoughi ◽  
Meng Li ◽  
Chao Hu ◽  
Cameron A. Mackenzie
Keyword(s):  
Reliability Analysis ◽  
Surrogate Model ◽  
Limit State ◽  
Efficient Estimation ◽  
High Dimensional ◽  
State Function ◽  
Performance Function ◽  
Highly Nonlinear ◽  
Computationally Expensive ◽  
Sample Points

Reliability analysis involving high-dimensional, computationally expensive, highly nonlinear performance functions is a notoriously challenging problem. In this paper, we tackle this problem by proposing a new method, high-dimensional reliability analysis (HDRA), in which a surrogate model is built to approximate a performance function that is high dimensional, computationally expensive, implicit and unknown to the user. HDRA first employs the adaptive univariate dimension reduction (AUDR) method to build a global surrogate model by adaptively tracking the important dimensions or regions. Then, the sequential exploration-exploitation with dynamic trade-off (SEEDT) method is utilized to locally refine the surrogate model by identifying additional sample points that are close to the critical region (i.e., the limit-state function) with high prediction uncertainty. The HDRA method has three advantages: (i) alleviating the curse of dimensionality and adaptively detecting important dimensions; (ii) capturing the interactive effects among variables on the performance function; and (iii) flexibility in choosing the locations of sample points. The performance of the proposed method is tested through two mathematical examples, the results of which suggest that the method can achieve accurate and computationally efficient estimation of reliability even when the performance function exhibits high dimensionality, high nonlinearity, and strong interactions among variables.

Response surface method strategies coupled with NLFEA for structural reliability analysis of prestressed bridges

2021 ◽  
Author(s):  
Silvia J. Sarmiento Nova ◽  
Jaime Gonzalez-Libreros ◽  
Gabriel Sas ◽  
Rafael A. Sanabria Díaz ◽  
Maria C. A. Texeira da Silva ◽  
...  
Keyword(s):  
Reliability Analysis ◽  
Response Surface ◽  
Response Surface Method ◽  
Structural Reliability ◽  
Limit State ◽  
Material Behavior ◽  
Nonlinear Material ◽  
State Function ◽  
Surface Method ◽  
Highly Nonlinear

<p>The Response Surface Method (RSM) has become an essential tool to solve structural reliability problems due to its accuracy, efficacy, and facility for coupling with Nonlinear Finite Element Analysis (NLFEA). In this paper, some strategies to improve the RSM efficacy without compromising its accuracy are tested. Initially, each strategy is implemented to assess the safety level of a highly nonlinear explicit limit state function. The strategy with the best results is then identified and used to carry out a reliability analysis of a prestressed concrete bridge, considering the nonlinear material behavior through NLFEA simulation. The calculated value of &#120573; is compared with the target value established in Eurocode for ULS. The results showed how RSM can be a practical methodology and how the improvements presented can reduce the computational cost of a traditional RSM giving a good alternative to simulation methods such as Monte Carlo.</p>

Study on Probabilistic Model of GH4133B for Fatigue-Creep Failure

2009 ◽  
Author(s):  
Dianyin Hu ◽  
Rongqiao Wang
Keyword(s):  
High Temperature ◽  
Reliability Analysis ◽  
Probabilistic Model ◽  
Low Cycle Fatigue ◽  
Limit State ◽  
Interactive Effect ◽  
Creep Damage ◽  
Sensitivity Index ◽  
State Function ◽  
Creep Failure

GH4133B is a nickel-base superalloy which was developed for use in the manufacture of aero-engine turbine disks and other high-temperature components. Since these components are operated at high temperature and under cyclic loading, damage resulting from fatigue-creep interaction is the main factor. The situation is often simulated in laboratories at high temperature low-cycle fatigue. The interactive effect between different loading levels should be considered. The fatigue-creep experiments for alloy GH4133B at 600 Celsius degree have been carried out at continuous cyclic creep (CF) loading to investigate the interaction of creep damage and fatigue damage. Fracture surfaces are examined under the scanning electron microscope (SEM). Then a nonlinear fatigue-creep failure criterion function proposed by Hongyin Mao is employed to fit the experimental data. The probabilistic model of GH4133B under CF loading is established based on the deterministic failure function. Firstly, the random variables influencing the fatigue-creep life and values of the distribution parameters are investigated. Then fatigue-creep damage interaction is discussed and a linear damage accumulation rule is considered, according to which the limit state function used to express the probability of failure is proposed. Lastly, reliability analysis under fatigue-creep failure is proceeded by applying analytical and simulation methods. Furthermore, the random variable with low sensitivity index through the sensitivity analysis can be treated as deterministic parameter during the reliability analysis and reliability design in order to improve the computing efficiency.

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.

scholarly journals Reliability-Based Serviceability Limit State Design of a Jacket Substructure for an Offshore Wind Turbine

Energies ◽  
2019 ◽  
Vol 12 (14) ◽  
pp. 2751 ◽  
Author(s):  
Jianhua Zhang ◽  
Won-Hee Kang ◽  
Ke Sun ◽  
Fushun Liu
Keyword(s):  
Correlation Analysis ◽  
Reliability Analysis ◽  
Limit State ◽  
Statistical Correlation ◽  
Offshore Wind ◽  
Offshore Wind Turbine ◽  
State Function ◽  
Optimized Design ◽  
Foundation Design ◽  
Serviceability Limit State

The development of a structurally optimized foundation design has become one of the main research objectives for offshore wind turbines (OWTs). The design process should be carried out in a probabilistic way due to the uncertainties involved, such as using parametric uncertainties regarding material and geometric properties, and model uncertainties in resistance prediction models and regarding environmental loads. Traditional simple deterministic checking procedures do not guarantee an optimized design because the associated uncertainties are not fully considered. In this paper, a reliability analysis framework is proposed to support the optimized design of jacket foundations for OWTs. The reliability analysis mainly considers the serviceability limit state of the structure according to the requirements of the code. The framework consists of two parts: (i) an important parameter identification procedure based on statistical correlation analysis and (ii) a finite element-simulation-based reliability estimation procedure. The procedure is demonstrated through a jacket structure design of a 3 MW OWT. The analysis results show that the statistical correlation analysis can help to identify the parameters necessary for the overall structural performance. The Latin hypercube sampling and the Monte Carlo simulation using FE models effectively and efficiently evaluate the reliability of the structure while not relying on a surrogate limit state function. A comparison between the proposed framework and the deterministic design shows that the framework can help to achieve a better result closer to the target reliability level.

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.

Fatigue Safety Factors for Flexible Risers Based on Case Specific Reliability Analysis

2005 ◽  
Author(s):  
Bernt J. Leira ◽  
Ragnar T. Igland ◽  
Gro S. Baarholm ◽  
Knut A. Farnes ◽  
Dick Percy
Keyword(s):  
Reliability Analysis ◽  
Limit State ◽  
State Function ◽  
Safety Factors ◽  
Fatigue Lifetime ◽  
Statistical Variation ◽  
Parametric Studies ◽  
Flexible Risers ◽  
Corrosive Environments ◽  
Wave Induced

In the present paper, fatigue safety factors for flexible risers are assessed. A procedure for reliability analysis of wave-induced fatigue is first described. The procedure is based on performing a number of parametric studies with respect to variables that influence the fatigue lifetime. The results of these parametric studies are subsequently combined with models describing the statistical scatter of the same parameters. By application of this procedure, the safety factors which are required in order to reach specific target reliability levels can be computed. Such safety factors are computed for three specific flexible riser configurations. Different SN -curves which correspond to different corrosive environments are considered. The percentwise contribution from each parameter to the total statistical variation of the limit state function is also quantified.

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.

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.

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