1,720,999 research outputs found
Bayesian updating : reducing epistemic uncertainty in hysteretic degradation behavior of steel tubular structures
Full text linkThis paper proposes a probabilistic framework for updating the governing parameters in the hysteretic constitutive model for tubular steel with strength degradation. The hysteretic constitutive model is formulated to track the strength degradation due to the local buckling of square hollow steel beam-columns imposed by cyclic loadings with large elastoplastic deformation. Despite various hysteretic laws that have been proposed to model the steel tubular strength degradation, limitations for determining parameter values remain in numerical analysis. The parameters are generally obfuscated by the inevitable epistemic uncertainties from material and geometric properties. The updating process of the material parameters is performed within the Bayesian framework employing the Markov chain Monte Carlo algorithm. The epistemic uncertainty involved in the computational procedure is initially represented as predefined intervals of the uncertain parameters. The proposed Markov chain Monte Carlo (MCMC) algorithm can generate samples from the posterior distributions of the parameters according to the experimental results. The epistemic uncertainty is hence significantly reduced by the Bayesian updating process such that the updated model is feasible to predict the degradation behavior of square hollow steel beam-columns subjected to cyclic loadings. The benchmark example indicates that the proposed framework can find the optimal path for updating key parameter values to accurately assess the condition of steel tubular structures in terms of the degradation behavior
Probabilistic approach for damping identification considering uncertainty in experimental modal analysis
No full textThe system identification technology is essentially an inverse procedure, starting from the experimentally measured response, to construct mass, stiffness, and damping matrices of the structure. However, the measurement inevitably contains uncertainties, which significantly impact the identified system characteristics, especially for damping terms. In the presence of experimental uncertainty, the aim of damping identification in this paper is not a single deterministic solution with maximum fidelity to a single experiment, but rathera set of optimized solutions with acceptable robustness to multiple uncertain experiments. To achieve this objective, an integrated approach combining deterministic identification and probabilistic calibration techniques is proposed. This approach starts from the properness condition of modes in a deterministic identification. A probabilistic estimation technique is performed on the preliminary identified data so that an uncertainty boundary is available for the calibration procedure where the genetic algorithm and classical optimization techniques are used. A comprehensive comparison metric for two continuous quantities is proposed as the objective function in the calibration procedure. Finally, a probabilistic validation metric is proposed to assess the stability of the calibrated damping matrix. In both simulated and experimental examples, the finally obtained matrices exhibit their robustness with regard to the experimental uncertainty.</p
Uncertainty quantification and propagation of crowd behaviour effects on pedestrian-induced vibrations of footbridges
Full text linkThe reliable prediction of pedestrian-induced vibration is essential for vibration serviceability assessment and further vibration mitigation design of footbridges. The response of the footbridge is governed by not only the structure dynamic model but also the crowd-induced load, which naturally involves randomness and uncertainty. It is consequently significant to appropriately characterize the uncertainties during the numerical modelling of the crowd behaviour effects on crowd-induced load. This work proposes a comprehensive approach to quantify the uncertainty from both the structure dynamic model and the crowd behaviour, and subsequently, to propagate the multiple sources of uncertainties from the input parameters to the response of the footbridge. The crowd behaviour is simulated using the social force model and translated to the crowd-induced load by combining with a single pedestrian induced walking force model. By decoupling the continuous model into several single degrees of freedom systems according to relevant modes in the vibration serviceability evaluation, the structure dynamic model of the footbridge is developed where the structural responses are calculated. In this paper, all the uncertain parameters are investigated together in a double-loop framework to perform uncertainty quantification and propagation in the form of probability-box (shortly termed as P-box). The uncertainty space of the peak structural responses is finally obtained by the Monte Carlo sampling and optimization in the outer loop and inner loop, respectively. Feasibility and performance of the overall approach are demonstrated by considering a real scale footbridge, and the failure probability of each comfort class regarding the peak acceleration response is also evaluated. Results show that, special attention should be paid on both the epistemic and aleatory uncertainties from the crowd behaviour in the vibration serviceability assessments of footbridges. The proposed uncertainty quantification framework may provide significant insights and improve the reliability for future vibration serviceability evaluations of footbridges by incorporating the crowd behaviour effects
Efficient variational Bayesian model updating by Bayesian active learning
Full text linkAs a main task of inverse problem, model updating has received more and more attention in the area of inspection, sensing, and monitoring technologies during the recent decades, where the estimation of posterior probability density function (PDF) of unknown model parameters is still challenging for expensive-to-evaluate models of interest. In this paper, a novel variational Bayesian inference method is proposed to approximate the real posterior PDF of unknown model parameters by using Gaussian mixture model and measurement responses. A Gaussian process regression model is first trained for approximating the logarithm of the product of likelihood function and prior PDF, with which, another Gaussian process model is induced for approximating the expensive evidence lower bound (ELBO). Then, two Bayesian numerical methods, i.e., Bayesian optimization and Bayesian quadrature, are combined sequentially as a novel Bayesian active learning method for searching the global optima of the parameters of the variational posterior density. The proposed method inherits the advantages of both Bayesian numerical methods, which includes good global convergence, much less number of simulator calls, etc. Three examples, including the dynamic model of a two degrees of freedom structures, the lubrication model of a hybrid journal bearing, and the dynamic model of an airplane structure, are introduced for demonstrating the relative merits of the proposed method. Results show that, given desired requirement of numerical accuracy, the proposed method is more efficient than the parallel methods
Distribution-free stochastic model updating of dynamic systems with parameter dependencies
Full text linkThis work proposes a distribution-free stochastic model updating framework to calibrate the joint probabilistic distribution of the multivariate correlated parameters. In this framework, the marginal distributions are defined as the staircase density functions and the correlation structure is described by the Gaussian copula function. The first four moments of the staircase density functions and the correlation coefficients are updated by an approximate Bayesian computation, in which the Bhattacharyya distance-based metric is proposed to define an approximate likelihood that is capable of capturing the stochastic discrepancy between model outputs and observations. The feasibility of the framework is demonstrated on two illustrative examples and a followed engineering application to the updating of a nonlinear dynamic system using observed time signals. The results demonstrate the capability of the proposed updating procedure in the very challenging condition where the prior knowledge about the distribution of the parameters is extremely limited (i.e., no information on the marginal distribution families and correlation structure is available)
Uncertainty quantification metrics with varying statistical information in model calibration and validation
No full textTest-analysis comparison metrics are mathematical functions that provide a quantitative measure of the agreement (or lack thereof) between numerical predictions and experimental measurements. While calibrating and validating models, the choice of a metric can significantly influence the outcome, yet the published research discussing the role of metrics, in particular, varying levels of statistical information the metrics can contain, has been limited. This paper calibrates and validates the model predictions using alternative metrics formulated based on three types of distancebased criteria: 1) Euclidian distance (i.e., the absolute geometric distance between two points), 2) Mahalanobis distance (i.e., the weighted distance that considers the correlations of two point clouds), and 3) Bhattacharyya distance (i.e., the statistical distance between two point clouds considering their probabilistic distributions). A comparative study is presented in the first case study, where the influence of various metrics, and the varying levels of statistical information they contain, on the predictions of the calibrated models is evaluated. In the second case study, an integrated application of the distance metrics is demonstrated through a cross-validation process with regard to the measurement variability.</p
Optimization or Bayesian strategy? Performance of the Bhattacharyya distance in different algorithms of stochastic model updating
No full textThe Bhattacharyya distance has been developed as a comprehensive uncertainty quantification metric by capturing multiple uncertainty sources from both numerical predictions and experimental measurements. This work pursues a further investigation of the performance of the Bhattacharyya distance in different methodologies for stochastic model updating, and thus to prove the universality of the Bhattacharyya distance in various currently popular updating procedures. The first procedure is the Bayesian model updating where the Bhattacharyya distance is utilized to define an approximate likelihood function and the transitional Markov chain Monte Carlo algorithm is employed to obtain the posterior distribution of the parameters. In the second updating procedure, the Bhattacharyya distance is utilized to construct the objective function of an optimization problem. The objective function is defined as the Bhattacharyya distance between the samples of numerical prediction and the samples of the target data. The comparison study is performed on a four degrees-of-freedom mass-spring system. A challenging task is raised in this example by assigning different distributions to the parameters with imprecise distribution coefficients. This requires the stochastic updating procedure to calibrate not the parameters themselves, but their distribution properties. The second example employs the GARTEUR SM-AG19 benchmark structure to demonstrate the feasibility of the Bhattacharyya distance in the presence of practical experiment uncertainty raising from measuring techniques, equipment, and subjective randomness. The results demonstrate the Bhattacharyya distance as a comprehensive and universal uncertainty quantification metric in stochastic model updating.</p
The role of the Bhattacharyya distance in stochastic model updating
Full text linkThe Bhattacharyya distance is a stochastic measurement between two samples and taking into account their probability distributions. The objective of this work is to further generalize the application of the Bhattacharyya distance as a novel uncertainty quantification metric by developing an approximate Bayesian computation model updating framework, in which the Bhattacharyya distance is fully embedded. The Bhattacharyya distance between sample sets is evaluated via a binning algorithm. And then the approximate likelihood function built upon the concept of the distance is developed in a two-step Bayesian updating framework, where the Euclidian and Bhattacharyya distances are utilized in the first and second steps, respectively. The performance of the proposed procedure is demonstrated with two exemplary applications, a simulated mass-spring example and a quite challenging benchmark problem for uncertainty treatment. These examples demonstrate a gain in quality of the stochastic updating by utilizing the superior features of the Bhattacharyya distance, representing a convenient, efficient, and capable metric for stochastic model updating and uncertainty characterization
The Bhattacharyya distance: Enriching the P-box in stochastic sensitivity analysis
Full text link© 2019 Elsevier Ltd The tendency of uncertainty analysis has promoted the transformation of sensitivity analysis from the deterministic sense to the stochastic sense. This work proposes a stochastic sensitivity analysis framework using the Bhattacharyya distance as a novel uncertainty quantification metric. The Bhattacharyya distance is utilised to provide a quantitative description of the P-box in a two-level procedure for both aleatory and epistemic uncertainties. In the first level, the aleatory uncertainty is quantified by a Monte Carlo process within the probability space of the cumulative distribution function. For each sample of the Monte Carlo simulation, the second level is performed to propagate the epistemic uncertainty by solving an optimisation problem. Subsequently, three sensitivity indices are defined based on the Bhattacharyya distance, making it possible to rank the significance of the parameters according to the reduction and dispersion of the uncertainty space of the system outputs. A tutorial case study is provided in the first part of the example to give a clear understanding of the principle of the approach with reproducible results. The second case study is the NASA Langley challenge problem, which demonstrates the feasibility of the proposed approach, as well as the Bhattacharyya distance metric, in solving such a large-scale, strong-nonlinear, and complex problem
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