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Xiaoping Du - One of the best experts on this subject based on the ideXlab platform.

  • Sequential Reliability-Based Optimization with Support Vector Machines
    Chinese Journal of Computational Mechanics, 2020
    Co-Authors: Yijun Wang, Xiongqing Yu, Xiaoping Du
    Abstract:

    Traditional reliability-based design optimization(RBDO)is either computational intensive or not accurate enough.In this work,a new RBDO method based on Support Vector Machines(SVM)is proposed.For reliability analysis,SVM is used to create a surrogate model of the Limit-State Function at the Most Probable Point(MPP).The uniqueness of the new method is the use of the gradient of the Limit-State Function at the MPP.This guarantees that the surrogate model not only passes through the MPP but also is tangent to the Limit-State Function at the MPP.Then Importance Sampling(IS)is used to calculate the probability of failure based on the surrogate model.This treatment significantly improves the accuracy of reliability analysis.For optimization,the Sequential Optimization and Reliability Assessment(SORA)is employed,which decouples deterministic optimization from the SVM reliability analysis.The decoupling makes RBDO more efficient.The two examples show that the new method is more accurate with a moderately increased computational cost.

  • Second Order Reliability Method for Time-Dependent Reliability Analysis Using Sequential Efficient Global Optimization
    Volume 2B: 45th Design Automation Conference, 2019
    Co-Authors: Zhangli Hu, Xiaoping Du
    Abstract:

    Abstract Reliability depends on time if the associated Limit-State Function includes time. A time-dependent reliability problem can be converted into a time-independent reliability problem by using the extreme value of the Limit-State Function. Then the first order reliability method can be used but it may produce a large error since the extreme Limit-State Function is usually highly nonlinear. This study proposes a new reliability method so that the second order reliability method can be applied to time-dependent reliability analysis for higher accuracy while maintaining high efficiency. The method employs sequential efficient global optimization to transform the time-dependent reliability analysis into the time-independent problem. The Hessian approximation and envelope theorem are used to obtain the second order information of the extreme Limit-State Function. Then the second order saddlepoint approximation is use to evaluate the reliability. The accuracy and efficiency of the proposed method are verified through numerical examples.

  • Saddlepoint approximation reliability method for quadratic Functions in normal variables
    Structural Safety, 2018
    Co-Authors: Zhangli Hu, Xiaoping Du
    Abstract:

    Abstract If the State of a component can be predicted by a Limit-State Function, the First and Second Order Reliability Methods are commonly used to calculate the reliability of the component. The latter method is more accurate because it approximates the Limit-State Function with a quadratic form in standard normal variables. To further improve the accuracy, this study develops a saddlepoint approximation reliability method that does not require additional transformations and approximations on the quadratic Function. Analytical equations are derived for the cumulant generating Function (CGF) of the Limit-State Function in standard normal variables, and then the saddlepoint is found by equating the derivative of the CGF to the Limit State. Thereafter a closed form solution to the reliability is available. The method can also apply to general nonlinear Limit-State Functions after they are approximated by a second order Taylor expansion. Examples show the better accuracy than the traditional second order reliability methods.

  • An efficient hybrid reliability analysis method with random and interval variables
    Engineering Optimization, 2015
    Co-Authors: Xiaoping Du
    Abstract:

    Random and interval variables often coexist. Interval variables make reliability analysis much more computationally intensive. This work develops a new hybrid reliability analysis method so that the probability analysis (PA) loop and interval analysis (IA) loop are decomposed into two separate loops. An efficient PA algorithm is employed, and a new efficient IA method is developed. The new IA method consists of two stages. The first stage is for monotonic Limit-State Functions. If the Limit-State Function is not monotonic, the second stage is triggered. In the second stage, the Limit-State Function is sequentially approximated with a second order form, and the gradient projection method is applied to solve the extreme responses of the Limit-State Function with respect to the interval variables. The efficiency and accuracy of the proposed method are demonstrated by three examples.

  • Improved Reliability-Based Optimization with Support Vector Machines and Its Application in Aircraft Wing Design
    Mathematical Problems in Engineering, 2015
    Co-Authors: Yu Wang, Xiongqing Yu, Xiaoping Du
    Abstract:

    A new reliability-based design optimization (RBDO) method based on support vector machines (SVM) and the Most Probable Point (MPP) is proposed in this work. SVM is used to create a surrogate model of the Limit-State Function at the MPP with the gradient information in the reliability analysis. This guarantees that the surrogate model not only passes through the MPP but also is tangent to the Limit-State Function at the MPP. Then, importance sampling (IS) is used to calculate the probability of failure based on the surrogate model. This treatment significantly improves the accuracy of reliability analysis. For RBDO, the Sequential Optimization and Reliability Assessment (SORA) is employed as well, which decouples deterministic optimization from the reliability analysis. The improved SVM-based reliability analysis is used to amend the error from linear approximation for Limit-State Function in SORA. A mathematical example and a simplified aircraft wing design demonstrate that the improved SVM-based reliability analysis is more accurate than FORM and needs less training points than the Monte Carlo simulation and that the proposed optimization strategy is efficient.

Karl Breitung - One of the best experts on this subject based on the ideXlab platform.

  • the geometry of Limit State Function graphs and subset simulation counterexamples
    Reliability Engineering & System Safety, 2019
    Co-Authors: Karl Breitung
    Abstract:

    Abstract In the last fifteen years the subset sampling method has often been used in reliability problems as a tool for calculating small probabilities. This method is extrapolating from an initial Monte Carlo estimate, for which the probability content of a failure domain found by a suitable higher level of the original Limit State Function. Then iteratively conditional probabilities are estimated for failures domains decreasing to the original failure domain. However, there are implied premises, regarding the structure of the failure domains, which must be fulfilled for the method to work properly. The examples studied in this paper demonstrate that inaccurate results might be obtained if the said premises are not fulfilled. This demonstrates that there are Limitations for the application of this method.

  • the geometry of Limit State Function graphs and subset simulation
    arXiv: Computation, 2017
    Co-Authors: Karl Breitung
    Abstract:

    In the last fifteen the subset sampling method has often been used in reliability problems as a tool for calculating small probabilities. This method is extrapolating from an initial Monte Carlo estimate for the probability content of a failure domain found by a suitable higher level of the original Limit State Function. Then iteratively conditional probabilities are estimated for failures domains decreasing to the original failure domain. But there are assumptions not immediately obvious about the structure of the failure domains which must be fulfilled that the method works properly. Here examples are studied that show that at least in some cases if these premises are not fulfilled, inaccurate results may be obtained. For the further development of the subset sampling method it is certainly desirable to find approaches where it is possible to check that these implicit assumptions are not violated. Also it would be probably important to develop further improvements of the concept to get rid of these Limitations.

  • Extrapolation, Invariance, Geometry and Subset Sampling
    14th International Probabilistic Workshop, 2016
    Co-Authors: Karl Breitung
    Abstract:

    In the last years the subset sampling method has often been used in reliability problems as a tool for calculating very small probabilities. The method extrapolates from an initial Monte Carlo estimate for the probability content of a failure domain found by a suitable higher level of the original Limit State Function. Then iteratively conditional probabilities are estimated for values of the Limit State Function decreasing to zero. But there are implicit assumptions about the structure of the failure domains which have to be fulfilled that the method works properly. It is shown by examples that at least in some cases if these assumptions are not fulfilled, erroneous results may be obtained. For the further development of the subset sampling concept it might be desirable to find approaches where it is possible to ascertain that these implicit assumptions are not violated or how to avoid by an increased computational effort misleading influences of the structure of the Limit State Functions.

N Narimanzadeh - One of the best experts on this subject based on the ideXlab platform.

  • reliability based optimal controller design for systems with probabilistic uncertain parameters using fuzzy Limit State Function
    Journal of Vibration and Control, 2015
    Co-Authors: A Jamali, Bahman Ahmadi, Mehdi Ghamati, N Narimanzadeh
    Abstract:

    In this paper, a fuzzy rule-based system (FRS) has been used for optimal reliability-based robust controller design for a two-mass-spring system with probabilistic uncertainties in its parameters. In this way, a multiobjective uniform-diversity genetic algorithm (MUGA) is first used to find a Pareto front of two-mass-spring system in a deterministic approach. This paper considers a two-mass-spring system under an impulse input. Two conflicting objective Functions in this model include settling time of the second mass and control effort exerted on the first mass. Consequently, such Pareto front is then obtained for a two-mass-spring system with probabilistic uncertainties in its parameters using the probabilities of failure of those objective Functions through a Monte Carlo simulation approach. It is shown that the FRS system removes the difficulty of selecting suitable crisp values and obligation due to a defining Limit State Function. Besides, the multiobjective Pareto optimization of such robust control...

R E Melchers - One of the best experts on this subject based on the ideXlab platform.

  • an efficient formulation for Limit State Function gradient calculation
    Computers & Structures, 1994
    Co-Authors: X L Guan, R E Melchers
    Abstract:

    Abstract In the first-order second moment (FOSM) reliability analysis, the gradients of the Limit State Function with respect to the basic random variables need to be calculated. For complex structures, these calculations can often be performed with the use of the probabilistic finite element (PFE) routines. However, for practical problems with a large number of basic random variables, the computation of the gradients is usually very expensive. This is particularly true in the FOSM analysis since the computation of the gradient vector is required to be repeated at each iteration step in the optimization algorithm. A new formulation, which reduces CPU time in computing the gradient vector without affecting the accuracy, is developed in this paper. For a simple example, direct comparison of the new technique with other methods that it is able to significantly reduce the CPU time and storage space requirements.

A Jamali - One of the best experts on this subject based on the ideXlab platform.

  • reliability based optimal controller design for systems with probabilistic uncertain parameters using fuzzy Limit State Function
    Journal of Vibration and Control, 2015
    Co-Authors: A Jamali, Bahman Ahmadi, Mehdi Ghamati, N Narimanzadeh
    Abstract:

    In this paper, a fuzzy rule-based system (FRS) has been used for optimal reliability-based robust controller design for a two-mass-spring system with probabilistic uncertainties in its parameters. In this way, a multiobjective uniform-diversity genetic algorithm (MUGA) is first used to find a Pareto front of two-mass-spring system in a deterministic approach. This paper considers a two-mass-spring system under an impulse input. Two conflicting objective Functions in this model include settling time of the second mass and control effort exerted on the first mass. Consequently, such Pareto front is then obtained for a two-mass-spring system with probabilistic uncertainties in its parameters using the probabilities of failure of those objective Functions through a Monte Carlo simulation approach. It is shown that the FRS system removes the difficulty of selecting suitable crisp values and obligation due to a defining Limit State Function. Besides, the multiobjective Pareto optimization of such robust control...