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Ning-cong Xiao - One of the best experts on this subject based on the ideXlab platform.
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adaptive kriging based efficient Reliability Method for structural systems with multiple failure modes and mixed variables
Computer Methods in Applied Mechanics and Engineering, 2020Co-Authors: Ning-cong Xiao, Kai Yuan, Chengning ZhouAbstract:Abstract The Reliability analysis of structural systems with multiple failure modes and mixed variables is a critical problem because of complex nonlinear correlations among failure modes (or components), huge computational burden of time-consuming implicit functions, and complex failure regions. In this paper, aleatory and epistemic uncertainties are considered simultaneously, and an efficient adaptive kriging-based Reliability Method is proposed for structural systems with multiple failure modes and mixed variables. Two new learning functions are developed as guidelines for selecting new training samples at each iteration. The proposed learning functions and corresponding stopping criteria are directly linked to system probability of failure; this allows the proposed Method to select new training samples efficiently To determine the lower and upper bounds of system probability of failure, the limit-state functions in the entire uncertainty space of interest are accurately constructed while avoiding complicated nested optimizations. The proposed Method has the following advantages: (1) the learning functions and stopping criteria are directly linked to system probability of failure, and the structure importance of components is also considered; (2) it requires fewer samples to achieve accurate results, and can be applied to small system probability of failure; (3) it is easy to use for extremely complex systems (e.g., bridge systems); (4) it can be applied to a system with multiple failure modes and mixed variables (e.g., mixture of random and p-box variables). The capabilities and efficiency of the proposed Method are validated through four numerical examples; results show that it has high applicability and accuracy.
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A new Reliability Method for small failure probability problems by combining the adaptive importance sampling and surrogate models
Computer Methods in Applied Mechanics and Engineering, 2020Co-Authors: Ning-cong Xiao, Hongyou Zhan, Kai YuanAbstract:Abstract Reliability analysis for structural systems with multiple failure modes and expensive-to-evaluate simulations is challenging. In this paper, a new and efficient system Reliability Method is proposed based on the adaptive importance sampling and kriging models. The Metropolis–Hastings (M–H) algorithm is used to construct several Markov chains to fully explore complex failure regions. A number of Markov chain states are selected as the center of the component importance sampling functions to generate samples for Reliability analysis. Based on the component importance sampling function of each selected chain state, the system importance sampling function is constructed with the weighting index. The system importance sampling function can be constructed effectively because it does not involve time-consuming simulations and the most probable point (MPP) search. The new learning function, which is directly linked to the system failure probability, is developed to adaptively select the best added samples for refining the kriging models at each iteration. The adaptive importance sampling Method and kriging models are well-combined for system Reliability analysis in the proposed Method. Compared with existing Methods, the proposed Method, generally, offers the following advantages: (1) The learning function and stopping criterion are directly linked to system failure probability; (2)the adaptive importance sampling and kriging models are well-combined to yield accurate results based on a small sample size for small failure probability problems; (3) the weights of sampling centers are considered, and the MPP search is not required at each iteration; (4) it is applicable for complex systems regardless of the structure and system failure probability level. Three numerical examples are analyzed, which demonstrate that the proposed Method is effective for complex system Reliability analysis.
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surrogate model based Reliability Method for structural systems with dependent truncated random variables
Proceedings of the Institution of Mechanical Engineers Part O: Journal of Risk and Reliability, 2017Co-Authors: Ning-cong Xiao, Libin Duan, Zhangchun TangAbstract:Calculating probability of failure and Reliability sensitivity for a structural system with dependent truncated random variables and multiple failure modes efficiently is a challenge mainly due to the complicated features and intersections for the multiple failure modes, as well as the correlated performance functions. In this article, a new surrogate-model-based Reliability Method is proposed for structural systems with dependent truncated random variables and multiple failure modes. Copula functions are used to model the correlation for truncated random variables. A small size of uniformly distribution samples in the supported intervals is generated to cover the entire uncertainty space fully and properly. An accurate surrogate model is constructed based on the proposed training points and support vector machines to approximate the relationships between the inputs and system responses accurately for almost the entire uncertainty space. The approaches to calculate probability of failure and Reliability sensitivity for structural systems with truncated random variables and multiple failure modes based on the constructed surrogate model are derived. The accuracy and efficiency of the proposed Method are demonstrated using two numerical examples.
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a novel Reliability Method for structural systems with truncated random variables
Structural Safety, 2014Co-Authors: Ning-cong Xiao, Yuanjian Yang, Hongzhong HuangAbstract:Uncertainty is usually modeled using random variable with certain probability distribution. However, the probability distributions of many random variables are often truncated in engineering applications. In the procedure of Reliability based design optimization for structural systems with truncated random variables, repeated function evaluations are required for different design points where the computational costs are extremely huge. In this paper, an efficient as well as novel Reliability Method is proposed for structural systems with truncated random variables which does not require repeated function evaluations for the different design points. Uniformly distributed samples are generated for truncated random variables in the supported intervals and design variables in the specified intervals to approximate cover the entire uncertain space fully. In order to avoid repeated function evaluations and improve computational efficiency, a surrogate model is established using back-propagation (BP) neural networks which can approximate the relationships between the inputs and system responses properly in almost entire uncertain space using the proposed given available data. The main advantages of the proposed Method are high accuracy and effectiveness in estimating the probability of failure under different design points which requires neither large samples nor the repeated function evaluations when compared to the existing Reliability Methods. Four numerical examples are investigated to demonstrate the effectiveness and accuracy of the proposed Method.
Nicolas Relun - One of the best experts on this subject based on the ideXlab platform.
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a combined importance sampling and kriging Reliability Method for small failure probabilities with time demanding numerical models
Reliability Engineering & System Safety, 2013Co-Authors: B Echard, Maurice Lemaire, Nicolas Gayton, Nicolas RelunAbstract:Abstract Applying Reliability Methods to a complex structure is often delicate for two main reasons. First, such a structure is fortunately designed with codified rules leading to a large safety margin which means that failure is a small probability event. Such a probability level is difficult to assess efficiently. Second, the structure mechanical behaviour is modelled numerically in an attempt to reproduce the real response and numerical model tends to be more and more time-demanding as its complexity is increased to improve accuracy and to consider particular mechanical behaviour. As a consequence, performing a large number of model computations cannot be considered in order to assess the failure probability. To overcome these issues, this paper proposes an original and easily implementable Method called AK-IS for active learning and Kriging-based Importance Sampling. This new Method is based on the AK-MCS algorithm previously published by Echard et al. [AK-MCS: an active learning Reliability Method combining Kriging and Monte Carlo simulation. Structural Safety 2011;33(2):145–54]. It associates the Kriging metamodel and its advantageous stochastic property with the Importance Sampling Method to assess small failure probabilities. It enables the correction or validation of the FORM approximation with only a very few mechanical model computations. The efficiency of the Method is, first, proved on two academic applications. It is then conducted for assessing the Reliability of a challenging aerospace case study submitted to fatigue.
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a combined importance sampling and kriging Reliability Method for small failure probabilities with time demanding numerical models
Reliability Engineering & System Safety, 2013Co-Authors: B Echard, Maurice Lemaire, Nicolas Gayton, Nicolas RelunAbstract:Abstract Applying Reliability Methods to a complex structure is often delicate for two main reasons. First, such a structure is fortunately designed with codified rules leading to a large safety margin which means that failure is a small probability event. Such a probability level is difficult to assess efficiently. Second, the structure mechanical behaviour is modelled numerically in an attempt to reproduce the real response and numerical model tends to be more and more time-demanding as its complexity is increased to improve accuracy and to consider particular mechanical behaviour. As a consequence, performing a large number of model computations cannot be considered in order to assess the failure probability. To overcome these issues, this paper proposes an original and easily implementable Method called AK-IS for active learning and Kriging-based Importance Sampling. This new Method is based on the AK-MCS algorithm previously published by Echard et al. [AK-MCS: an active learning Reliability Method combining Kriging and Monte Carlo simulation. Structural Safety 2011;33(2):145–54]. It associates the Kriging metamodel and its advantageous stochastic property with the Importance Sampling Method to assess small failure probabilities. It enables the correction or validation of the FORM approximation with only a very few mechanical model computations. The efficiency of the Method is, first, proved on two academic applications. It is then conducted for assessing the Reliability of a challenging aerospace case study submitted to fatigue.
B Echard - One of the best experts on this subject based on the ideXlab platform.
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a combined importance sampling and kriging Reliability Method for small failure probabilities with time demanding numerical models
Reliability Engineering & System Safety, 2013Co-Authors: B Echard, Maurice Lemaire, Nicolas Gayton, Nicolas RelunAbstract:Abstract Applying Reliability Methods to a complex structure is often delicate for two main reasons. First, such a structure is fortunately designed with codified rules leading to a large safety margin which means that failure is a small probability event. Such a probability level is difficult to assess efficiently. Second, the structure mechanical behaviour is modelled numerically in an attempt to reproduce the real response and numerical model tends to be more and more time-demanding as its complexity is increased to improve accuracy and to consider particular mechanical behaviour. As a consequence, performing a large number of model computations cannot be considered in order to assess the failure probability. To overcome these issues, this paper proposes an original and easily implementable Method called AK-IS for active learning and Kriging-based Importance Sampling. This new Method is based on the AK-MCS algorithm previously published by Echard et al. [AK-MCS: an active learning Reliability Method combining Kriging and Monte Carlo simulation. Structural Safety 2011;33(2):145–54]. It associates the Kriging metamodel and its advantageous stochastic property with the Importance Sampling Method to assess small failure probabilities. It enables the correction or validation of the FORM approximation with only a very few mechanical model computations. The efficiency of the Method is, first, proved on two academic applications. It is then conducted for assessing the Reliability of a challenging aerospace case study submitted to fatigue.
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a combined importance sampling and kriging Reliability Method for small failure probabilities with time demanding numerical models
Reliability Engineering & System Safety, 2013Co-Authors: B Echard, Maurice Lemaire, Nicolas Gayton, Nicolas RelunAbstract:Abstract Applying Reliability Methods to a complex structure is often delicate for two main reasons. First, such a structure is fortunately designed with codified rules leading to a large safety margin which means that failure is a small probability event. Such a probability level is difficult to assess efficiently. Second, the structure mechanical behaviour is modelled numerically in an attempt to reproduce the real response and numerical model tends to be more and more time-demanding as its complexity is increased to improve accuracy and to consider particular mechanical behaviour. As a consequence, performing a large number of model computations cannot be considered in order to assess the failure probability. To overcome these issues, this paper proposes an original and easily implementable Method called AK-IS for active learning and Kriging-based Importance Sampling. This new Method is based on the AK-MCS algorithm previously published by Echard et al. [AK-MCS: an active learning Reliability Method combining Kriging and Monte Carlo simulation. Structural Safety 2011;33(2):145–54]. It associates the Kriging metamodel and its advantageous stochastic property with the Importance Sampling Method to assess small failure probabilities. It enables the correction or validation of the FORM approximation with only a very few mechanical model computations. The efficiency of the Method is, first, proved on two academic applications. It is then conducted for assessing the Reliability of a challenging aerospace case study submitted to fatigue.
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ak mcs an active learning Reliability Method combining kriging and monte carlo simulation
Structural Safety, 2011Co-Authors: B Echard, Nicolas Gayton, Maurice LemaireAbstract:Abstract An important challenge in structural Reliability is to keep to a minimum the number of calls to the numerical models. Engineering problems involve more and more complex computer codes and the evaluation of the probability of failure may require very time-consuming computations. Metamodels are used to reduce these computation times. To assess Reliability, the most popular approach remains the numerous variants of response surfaces. Polynomial Chaos [1] and Support Vector Machine [2] are also possibilities and have gained considerations among researchers in the last decades. However, recently, Kriging, originated from geostatistics, have emerged in Reliability analysis. Widespread in optimisation, Kriging has just started to appear in uncertainty propagation [3] and Reliability [4] , [5] studies. It presents interesting characteristics such as exact interpolation and a local index of uncertainty on the prediction which can be used in active learning Methods. The aim of this paper is to propose an iterative approach based on Monte Carlo Simulation and Kriging metamodel to assess the Reliability of structures in a more efficient way. The Method is called AK-MCS for Active learning Reliability Method combining Kriging and Monte Carlo Simulation. It is shown to be very efficient as the probability of failure obtained with AK-MCS is very accurate and this, for only a small number of calls to the performance function. Several examples from literature are performed to illustrate the Methodology and to prove its efficiency particularly for problems dealing with high non-linearity, non-differentiability, non-convex and non-connex domains of failure and high dimensionality.
Behrooz Keshtegar - One of the best experts on this subject based on the ideXlab platform.
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Reliability analysis of corroded pipelines: Novel adaptive conjugate first order Reliability Method
Journal of Loss Prevention in the Process Industries, 2019Co-Authors: Behrooz Keshtegar, Mohamed El Amine Ben Seghier, Shun-peng Zhu, Rouzbeh Abbassi, Nguyen-thoi TrungAbstract:Abstract The burst pressure of oil and gas pipelines with corrosion defects is the major failure mode of these structures. Structural Reliability analysis is normally conducted to evaluate the robust design-based safe levels of corroded pipelines using the probabilistic failure model. In the current work, the abilities for robustness and efficiency of first order Reliability Method (FORM) formulas are investigated for corroded mid-strength grade steel pipes. These Methods are mainly enhance FORM algorithms-based steepest descent search direction as directional stability transformation Method (DSTM), finite-step length (FSL), finite-step adaptive length (FAL) and conjugate steepest descent search direction as conjugate HL-RF (CHL-RF), conjugate finite-step length (CFSL) and a proposed adaptive conjugate finite step length (ACFSL). In proposed ACFSL algorithm, the FORM formula is adaptively enhanced using the dynamical conjugate search direction to adapt the new iterations for the burst pressure failure mode which is computed using a probabilistic combined by plastic flow theory-based average shear stress yield criterion and remaining stress factor-based semi-elliptical defects. Comparative results indicate that three algorithms e.g. FAL, CFSL and ACFSL are the perfect convergence performances for Reliability analysis of corroded pipeline compared to other formulas, while ACFSL provides the superior performances in term of efficiency and robustness. The safety level of these structures is highly sensitive to the corrosion defect depths and operating pressure.
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Refined first-order Reliability Method using cross-entropy optimization Method
Engineering with Computers, 2018Co-Authors: Hamed Ghohani Arab, Mohsen Rashki, Mehdi Rostamian, Alireza Ghavidel, Hossein Shahraki, Behrooz KeshtegarAbstract:Generally, the first-order Reliability Method (FORM) is an efficient and accurate Reliability Method for problems with linear limit state functions (LSFs). It is showed that the FORM formula may produce inaccurate results when the LSF is defined by mathematical forms introduced as gray function. Thus, the original FORM formula may provide the results with huge errors. In this paper, a probabilistic optimization model as refined FORM (R-FORM) is presented to search most probable failure point (MPP) with the accurate results for gray LSFs. The cross-entropy optimization (CEO) Method is utilized to search MPP in proposed R-FORM model. Several Reliability problems are applied to illustrate the accuracy of the R-FORM compared to the conventional FORM formula. Results illustrate that the R-FORM provides more accurate results than the FORM for gray performance functions.
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enhanced sequential approximate programming using second order Reliability Method for accurate and efficient structural Reliability based design optimization
Applied Mathematical Modelling, 2018Co-Authors: Zeng Meng, Huanlin Zhou, Behrooz KeshtegarAbstract:Abstract Second-order Reliability Method (SORM) can provide sufficient accuracy for evaluating the probabilistic constraints in Reliability-based design optimization (RBDO). However, the application of SORM in RBDO significantly increases the computational burden, as it is necessary to calculate the second-order sensitivities of the performance function. In order to achieve equal efficiency to that of the first-order Reliability Method-based RBDO approach, enhanced sequential approximate programming (ESAP) is proposed by implementing the SORM-based RBDO Method. Based on the diagonal quadratic approximation Method, the Hessian matrix is calculated without generating additional computational costs for providing the design sensitivity analysis of probabilistic constraints within the same iterations. Furthermore, ESAP is applied to the Reliability-based topology optimization domain, and five numerical benchmark RBDO problems with two complex engineering examples are studied. The proposed ESAP is compared with other RBDO Methods, including the Reliability index approach, performance measure approach, sequential optimization and Reliability assessment Method, and SAP, and the results demonstrate the superiority of the proposed ESAP.
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Fuzzy relaxed-finite step size Method to enhance the instability of the fuzzy first-order Reliability Method using conjugate discrete map
Nonlinear Dynamics, 2018Co-Authors: Behrooz Keshtegar, Mansour BagheriAbstract:Fuzzy Reliability analysis can be implemented using two discrete optimization maps in the processes of Reliability and fuzzy analysis. Actually, the efficiency and robustness of the iterative Reliability Methods are two main factors in the fuzzy-based Reliability analysis due to the huge computational burdens and unstable results. In the structural fuzzy Reliability analysis, the first-order Reliability Method (FORM) using discrete nonlinear map can provide a C membership function. In this paper, a discrete nonlinear conjugate map is proposed using a relaxed-finite step size Method for fuzzy structural Reliability analysis, namely Fuzzy conjugate relaxed-finite step size Method fuzzy CRS. A discrete conjugate map is stabilized using two adaptive factors to compute the relaxed factor and step size in FORM. The framework of the proposed fuzzy structural Reliability Method is established using two linked iterative discrete maps as an outer loop, which constructs the membership function of the response using alpha level set optimization based on genetic operator, and the inner loop, implemented for Reliability analysis using proposed conjugate relaxed-finite step size Method. The fuzzy CRS and fuzzy HL-RF Methods are compared to evaluate the membership functions of five structural problems with highly nonlinear limit state functions. Results demonstrated that the fuzzy CRS Method is computationally more efficient and is strongly more robust than the HL-RF for fuzzy-based Reliability analysis of the nonlinear structural Reliability problems.
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An efficient-robust structural Reliability Method by adaptive finite-step length based on Armijo line search
Reliability Engineering & System Safety, 2018Co-Authors: Behrooz Keshtegar, Subrata ChakrabortyAbstract:Abstract The robustness of iterative formula as well as its computational efficiency is the essential characteristic of interest for effective Reliability analysis of structures by first order Reliability Method (FORM). A robust and efficient iterative algorithm termed as finite-based Armijo search direction (FAL) Method is proposed in the present study for FORM-based structural Reliability analysis. A finite-step size is proposed using the Armijo rule and sufficient descent condition to achieve the stabilization of the FORM algorithm. The FAL is adaptively adjusted based on the information obtained from the iterative algorithm at each iteration and Armijo rule. The robustness and efficiency of the proposed FAL Method is elucidated using several problems. The results obtained by the proposed Method are compared with various existing Reliability Methods based on steepest descent search direction. The results of the numerical study indicate that the FAL approach is more robust and efficient than the other existing FORM schemes and improves the robustness of FORM formula. Thus, the FAL can be successfully implemented as a robust FORM-based iterative Reliability analysis procedure.
Maurice Lemaire - One of the best experts on this subject based on the ideXlab platform.
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a combined importance sampling and kriging Reliability Method for small failure probabilities with time demanding numerical models
Reliability Engineering & System Safety, 2013Co-Authors: B Echard, Maurice Lemaire, Nicolas Gayton, Nicolas RelunAbstract:Abstract Applying Reliability Methods to a complex structure is often delicate for two main reasons. First, such a structure is fortunately designed with codified rules leading to a large safety margin which means that failure is a small probability event. Such a probability level is difficult to assess efficiently. Second, the structure mechanical behaviour is modelled numerically in an attempt to reproduce the real response and numerical model tends to be more and more time-demanding as its complexity is increased to improve accuracy and to consider particular mechanical behaviour. As a consequence, performing a large number of model computations cannot be considered in order to assess the failure probability. To overcome these issues, this paper proposes an original and easily implementable Method called AK-IS for active learning and Kriging-based Importance Sampling. This new Method is based on the AK-MCS algorithm previously published by Echard et al. [AK-MCS: an active learning Reliability Method combining Kriging and Monte Carlo simulation. Structural Safety 2011;33(2):145–54]. It associates the Kriging metamodel and its advantageous stochastic property with the Importance Sampling Method to assess small failure probabilities. It enables the correction or validation of the FORM approximation with only a very few mechanical model computations. The efficiency of the Method is, first, proved on two academic applications. It is then conducted for assessing the Reliability of a challenging aerospace case study submitted to fatigue.
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a combined importance sampling and kriging Reliability Method for small failure probabilities with time demanding numerical models
Reliability Engineering & System Safety, 2013Co-Authors: B Echard, Maurice Lemaire, Nicolas Gayton, Nicolas RelunAbstract:Abstract Applying Reliability Methods to a complex structure is often delicate for two main reasons. First, such a structure is fortunately designed with codified rules leading to a large safety margin which means that failure is a small probability event. Such a probability level is difficult to assess efficiently. Second, the structure mechanical behaviour is modelled numerically in an attempt to reproduce the real response and numerical model tends to be more and more time-demanding as its complexity is increased to improve accuracy and to consider particular mechanical behaviour. As a consequence, performing a large number of model computations cannot be considered in order to assess the failure probability. To overcome these issues, this paper proposes an original and easily implementable Method called AK-IS for active learning and Kriging-based Importance Sampling. This new Method is based on the AK-MCS algorithm previously published by Echard et al. [AK-MCS: an active learning Reliability Method combining Kriging and Monte Carlo simulation. Structural Safety 2011;33(2):145–54]. It associates the Kriging metamodel and its advantageous stochastic property with the Importance Sampling Method to assess small failure probabilities. It enables the correction or validation of the FORM approximation with only a very few mechanical model computations. The efficiency of the Method is, first, proved on two academic applications. It is then conducted for assessing the Reliability of a challenging aerospace case study submitted to fatigue.
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ak mcs an active learning Reliability Method combining kriging and monte carlo simulation
Structural Safety, 2011Co-Authors: B Echard, Nicolas Gayton, Maurice LemaireAbstract:Abstract An important challenge in structural Reliability is to keep to a minimum the number of calls to the numerical models. Engineering problems involve more and more complex computer codes and the evaluation of the probability of failure may require very time-consuming computations. Metamodels are used to reduce these computation times. To assess Reliability, the most popular approach remains the numerous variants of response surfaces. Polynomial Chaos [1] and Support Vector Machine [2] are also possibilities and have gained considerations among researchers in the last decades. However, recently, Kriging, originated from geostatistics, have emerged in Reliability analysis. Widespread in optimisation, Kriging has just started to appear in uncertainty propagation [3] and Reliability [4] , [5] studies. It presents interesting characteristics such as exact interpolation and a local index of uncertainty on the prediction which can be used in active learning Methods. The aim of this paper is to propose an iterative approach based on Monte Carlo Simulation and Kriging metamodel to assess the Reliability of structures in a more efficient way. The Method is called AK-MCS for Active learning Reliability Method combining Kriging and Monte Carlo Simulation. It is shown to be very efficient as the probability of failure obtained with AK-MCS is very accurate and this, for only a small number of calls to the performance function. Several examples from literature are performed to illustrate the Methodology and to prove its efficiency particularly for problems dealing with high non-linearity, non-differentiability, non-convex and non-connex domains of failure and high dimensionality.
