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Yongming Liu - One of the best experts on this subject based on the ideXlab platform.

  • efficient high dimensional material Reliability analysis with explicit voxel level stochastic microstructure representation
    Applied Mathematical Modelling, 2021
    Co-Authors: Yi Gao, Yang Jiao, Yongming Liu
    Abstract:

    Abstract A novel efficient Methodology for probabilistic material Reliability analysis considering fine-scale microstructure stochasticity is proposed in this paper. Integrated computational material engineering requires efficient multiscale computational capabilities to enable computational design and validation. Two critical challenges are identified: handling uncertainties from microstructures and material properties; and handling the “curse of dimensionality” for probabilistic solvers. The proposed study addresses these two critical challenges. First, an analytical and hierarchical uncertainty quantification Method is proposed for the explicit stochastic microstructure representation at the voxel-level. The hierarchy of uncertainties from both phase maps and uncertainties within each phase is modeled using an explicit Gaussian mixture random field. Analytical approximation for the arbitrary non-Gaussian random field is derived, which can facilitate the computation of gradient information in optimization. Following this, an efficient probabilistic solver using adjoint First-Order Reliability Method combining the importance sampling is derived by formulating the material Reliability analysis as a constrained optimization problem. The adjoint Method is used to efficiently evaluate the responses and exact gradients with the help of the analytical Gaussian mixture random field. Several numerical examples for material Reliability calculation with high-dimensional (voxel-level) random fields are subsequently employed to demonstrate and validate the proposed Methodology. The results of the proposed Method are quantitatively compared to those obtained via the classical First-Order Reliability Method, direct Monte Carlo simulation, subset simulation, and the sequential importance sampling Method. The comparisons indicate that the proposed Method possesses high efficiency for high-dimensional material Reliability problems.

  • Equivalent Stress Transformation for Efficient Probabilistic Fatigue-Crack Growth Analysis under Variable Amplitude Loadings
    Journal of Aerospace Engineering, 2016
    Co-Authors: Yibing Xiang, Yongming Liu
    Abstract:

    AbstractA general probabilistic fatigue-crack growth prediction Methodology for accurate and efficient damage prognosis is proposed in this paper. The Methodology is based on an equivalent stress transformation and the inverse First-Order Reliability Method (IFORM). The equivalent stress transformation aims to transform the random variable amplitude loading to an equivalent constant amplitude loading spectrum. The proposed transformation avoids the cycle-by-cycle calculation under general random variable amplitude loadings. An IFORM is used to evaluate the probabilistic fatigue-crack growth behavior and to further enhance the computational efficiency. The computational cost of the proposed study is significantly reduced compared with the direct Monte Carlo simulation. Thus, the proposed Method is very suitable for real-time damage prognosis because of its high computational efficiency. Numerical examples are used to demonstrate the proposed Method. Various experimental data under variable amplitude loadin...

  • an efficient analytical bayesian Method for Reliability and system response updating based on laplace and inverse first order Reliability computations
    Reliability Engineering & System Safety, 2012
    Co-Authors: Xuefei Guan, Ratneshwar Jha, Yongming Liu
    Abstract:

    This paper presents an efficient analytical Bayesian Method for Reliability and system response updating without using simulations. The Method includes additional information such as measurement data via Bayesian modeling to reduce estimation uncertainties. Laplace approximation Method is used to evaluate Bayesian posterior distributions analytically. An efficient algorithm based on inverse First-Order Reliability Method is developed to evaluate system responses given a Reliability index or confidence interval. Since the proposed Method involves no simulations such as Monte Carlo or Markov chain Monte Carlo simulations, the overall computational efficiency improves significantly, particularly for problems with complicated performance functions. A practical fatigue crack propagation problem with experimental data, and a structural scale example are presented for Methodology demonstration. The accuracy and computational efficiency of the proposed Method are compared with traditional simulation-based Methods.

  • application of inverse first order Reliability Method for probabilistic fatigue life prediction
    Probabilistic Engineering Mechanics, 2011
    Co-Authors: Yibing Xiang, Yongming Liu
    Abstract:

    Abstract A general probabilistic life prediction Methodology for accurate and efficient fatigue prognosis is proposed in this paper. The proposed Methodology is based-on an inverse First-Order Reliability Method (IFORM) to evaluate the fatigue life at an arbitrary Reliability level. This formulation is different from the forward Reliability problem, which aims to calculate the failure probability at a fixed time instant. The variables in the fatigue prognosis problem are separated into two categories, i.e., random variables and index variables. An efficient searching algorithm for fatigue life prediction is developed to find the corresponding index variable at a certain confidence level. Numerical examples using direct Monte Carlo simulation and the proposed IFORM Method are compared for algorithm verification. Following this, various experimental data for metallic materials are used for model prediction validation.

Behrooz Keshtegar - One of the best experts on this subject based on the ideXlab platform.

  • rm5tree radial basis m5 model tree for accurate structural Reliability analysis
    Reliability Engineering & System Safety, 2018
    Co-Authors: Behrooz Keshtegar, Ozgur Kisi
    Abstract:

    Abstract The surrogate models-based prediction of performance functions is an efficient and accurate Methodology in structural Reliability analyses. In this paper, the M5 model tree (M5Tree) is improved based on radial basis training data set and it is named as Radial basis M5Tree (RM5Tree). To predict the performance function, the random input variables are transferred from ordinal space to radial space using several effective points for nonlinear calibrated model of RM5Tree. The input datasets are controlled using the radial dataset for high-dimensional Reliability problems to reduce computational efforts to evaluate the performance function. The abilities of RM5Tree using Monte Carlo Simulation (MCS) with respect to accuracy and efficiency are investigated through five nonlinear Reliability problems. The results indicate that the proposed RM5Tree performs superior manner in accuracy and efficiency compared to the M5Tree, response surface Method (RSM) and first order Reliability Method.

  • enhanced sequential approximate programming using second order Reliability Method for accurate and efficient structural Reliability based design optimization
    Applied Mathematical Modelling, 2018
    Co-Authors: Zeng Meng, Huanlin Zhou, Behrooz Keshtegar
    Abstract:

    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.

  • a hybrid self adaptive conjugate first order Reliability Method for robust structural Reliability analysis
    Applied Mathematical Modelling, 2018
    Co-Authors: Behrooz Keshtegar, Subrata Chakraborty
    Abstract:

    Abstract The traditional First Order Reliability Method (FORM) using steepest descent search direction may yield unstable solutions due to periodic nature and chaos for Reliability analysis problems involving highly nonlinear performance functions. A conjugate search direction approach is attempted in the present study to overcome such problem of the FORM for Most Probable Point (MPP) search. Two iterative FORM schemes are investigated based on conjugate descent direction using self-adaptive conjugate (SAC) and hybrid self- adaptive conjugate (HSAC) search directions for estimating Reliability index. The SAC is proposed using Fletcher and Reeves (FR) Method and an adaptive conjugate scalar factor to improve the efficiency of the FR Method for Reliability analysis of highly nonlinear performance function. The HSAC is adaptively computed using FR and SAC Methods to improve the robustness and efficiency of the FORM formula. The effectiveness of the proposed SAC and HSAC approaches are studied compare to the traditional FORM algorithms through several numerical examples. The proposed Methods based on conjugate search direction are found to be more efficient and robust than the usual FORM algorithms.

  • a hybrid relaxed first order Reliability Method for efficient structural Reliability analysis
    Structural Safety, 2017
    Co-Authors: Behrooz Keshtegar, Zeng Meng
    Abstract:

    Abstract The Hasofer-Lind and Rakwitz-Fiessler (HL-RF) algorithm is widely used for structural Reliability analysis in First-Order moment Method (FORM). However, it meets non-convergence problem including generating periodic and chaotic solutions for highly nonlinear limit state function. In this paper, relaxed HL-RF (RHL-RF) is developed based on a relaxed factor, which is dynamically computed by the second-order interpolation between zero and one. A hybrid relaxed HL-RF (HRHL-RF) Method is proposed, in which the HL-RF and RHL-RF are adaptively implemented by using an angle criterion to improve the robustness and efficiency of FORM formula. The angle condition is simply calculated based on the results from the new and previous points. Finally, the performances in terms of robustness and efficiency of the HRHL-RF are compared with several existing FORM Methods through five mathematical and structural examples. The results indicate that HRHL-RF Method is more robust than the HL-RF and more efficient than other existing Methods.

  • a hybrid conjugate finite step length Method for robust and efficient Reliability analysis
    Applied Mathematical Modelling, 2017
    Co-Authors: Behrooz Keshtegar
    Abstract:

    Abstract The robustness and efficiency of the First-Order Reliability Method (FORM) are the important issues in the structural Reliability analysis. In this paper, a hybrid conjugate search direction with finite-step length is proposed to improve the efficiency and robustness of FORM, namely hybrid conjugate finite-step length (CFSL-H). The conjugate scalar factor in CFSL-H is adaptively updated using two conjugate Methods with a dynamic participation factor. The accuracy, efficiency and robustness of the CFSL-H are illustrated through the nonlinear explicit and structural implicit limit state functions with normal and non-normal random variables. The results illustrated that the proposed CFSL-H algorithm is more robust, efficient and accurate than the modified existing FORM algorithms for complex structural problems.

Martin Pendola - One of the best experts on this subject based on the ideXlab platform.

  • time variant finite element Reliability analysis application to the durability of cooling towers
    Structural Safety, 2005
    Co-Authors: Bruno Sudret, G. Defaux, Martin Pendola
    Abstract:

    Durability of natural-draught cooling towers is investigated using finite element Reliability analysis. A response surface of the linear finite element model is first derived from mechanical considerations. This surface is explicit and exact under certain conditions and requires a single multi-load finite element analysis. This leads to an analytical formulation of the Reliability problem. The influence of concrete carbonation and the induced rebars corrosion is then studied in the framework of time-variant Reliability analysis. It is shown that the problem reduces to a sequence of time-invariant problems that can be solved using the First-Order Reliability Method (FORM). The evolution in time of the probability of failure in a single point is computed as well as sensitivity factors. Finally, an attempt to introducing space-variant Reliability is made. The great difference between the numerical results obtained in the first and in the second approach is emphasized.

Guedes C Soares - One of the best experts on this subject based on the ideXlab platform.

  • fatigue Reliability of a stiffened panel subjected to correlated crack growth
    Structural Safety, 2012
    Co-Authors: G.q. Feng, Yordan Garbatov, Guedes C Soares
    Abstract:

    The objective of this work is to analyze the fatigue Reliability of a stiffened panel subjected to the growth of correlated cracks. A probabilistic crack growth model is applied, allowing for the existence of multiple cracks both in the stiffener and in the plate, accounting for the correlation between them. The geometry functions of the correlated cracks in the plate and in the stiffener are defined from calculations of stress intensity factors applying the finite element Method. Monte Carlo simulations are used to define the statistical descriptions of crack growth. The failure probability assessment is performed based on a First Order Reliability Method (FORM), in which the residual strength of the plate and stiffener in the stiffened panel are formulated in terms of the crack tip opening displacement. The formulation is extended to account for inspections, updating the probability of failure with its outcomes. Various parameters related to the quality of manufacture, inspections, time interval between inspection, load level and target Reliability acceptance are studied.

Kai Goebel - One of the best experts on this subject based on the ideXlab platform.

  • Uncertainty quantification in remaining useful life prediction using First-Order Reliability Methods
    IEEE Transactions on Reliability, 2014
    Co-Authors: Swaminathan Sankararaman, Matthew J. Daigle, Kai Goebel
    Abstract:

    In this paper, we investigate the use of First-Order Reliability Methods to quantify the uncertainty in the remaining useful life (RUL) estimate of components used in engineering applications. The prediction of RUL is affected by several sources of uncertainty, and it is important to systematically quantify their combined effect on the RUL prediction in order to aid risk assessment, risk mitigation, and decision-making. While sampling-based algorithms have been conventionally used for quantifying the uncertainty in RUL, analytical approaches are computationally cheaper, and sometimes they are better suited for online decision-making. Exact analytical algorithms may not be available for practical engineering applications, but effective approximations can be made using First-Order Reliability Methods. This paper describes three First-Order Reliability-based Methods for RUL uncertainty quantification: First-Order second moment Method (FOSM), the First-Order Reliability Method (FORM), and the inverse First-Order Reliability Method (inverse-FORM). The inverse-FORM Methodology is particularly useful in the context of online health monitoring, and this Method is illustrated using the power system of an unmanned aerial vehicle, where the goal is to predict the end of discharge of a lithium-ion battery. [ABSTRACT FROM AUTHOR]

  • Uncertainty Quantification in Remaining Useful Life of Aerospace Components using State Space Models and Inverse FORM
    54th AIAA ASME ASCE AHS ASC Structures Structural Dynamics and Materials Conference, 2013
    Co-Authors: Shankar Sankararaman, Kai Goebel
    Abstract:

    This paper investigates the use of the inverse First-Order Reliability Method (inverse- FORM) to quantify the uncertainty in the remaining useful life (RUL) of aerospace components. The prediction of remaining useful life is an integral part of system health prognosis, and directly helps in online health monitoring and decision-making. However, the prediction of remaining useful life is affected by several sources of uncertainty, and therefore it is necessary to quantify the uncertainty in the remaining useful life prediction. While system parameter uncertainty and physical variability can be easily included in inverse-FORM, this paper extends the Methodology to include: (1) future loading uncertainty, (2) process noise; and (3) uncertainty in the state estimate. The inverse-FORM Method has been used in this paper to (1) quickly obtain probability bounds on the remaining useful life prediction; and (2) calculate the entire probability distribution of remaining useful life prediction, and the results are verified against Monte Carlo sampling. The proposed Methodology is illustrated using a numerical example.