UNCERTAINTY QUANTIFICATION AND GLOBAL SENSITIVITY ANALYSIS OF SEISMIC FRAGILITY CURVES USING KRIGING

Seismic fragility analysis of jacket type offshore platforms considering soil-pile-structure interaction

The aim of this article is to study the reliability analysis, parametric reliability sensitivity analysis and global reliability sensitivity analysis of structures with extremely rare failure events. First, the global reliability sensitivity indices are restudied, and we show that the total effect index can also be interpreted as the effect of randomly copying each individual input variable on the failure surface. Second, a new method, denoted as Active learning Kriging Markov Chain Monte Carlo (AK-MCMC), is developed for adaptively approximating the failure surface with active learning Kriging surrogate model as well as dynamically updated Monte Carlo or Markov chain Monte Carlo populations. Third, the AK-MCMC procedure combined with the quasi-optimal importance sampling procedure is extended for estimating the failure probability and the parametric reliability sensitivity and global reliability sensitivity indices. For estimating the global reliability sensitivity indices, two new importance sampling estimators are derived. The AK-MCMC procedure can be regarded as a combination of the classical Monte Carlo Simulation (AK-MCS) and subset simulation procedures, but it is much more effective when applied to extremely rare failure events. Results of test examples show that the proposed method can accurately and robustly estimate the extremely small failure probability (e.g. 1e–9) as well as the related parametric reliability sensitivity and global reliability sensitivity indices with several dozens of function calls.

Machine learning (ML) has been leveraged to tackle a diverse range of tasks in almost all branches of nuclear engineering. Many of the successes in ML applications can be attributed to the recent performance breakthroughs in deep learning and the growing availability of computational power, data, and easy-to-use ML libraries. However, these empirical successes have often outpaced our formal understanding of the ML algorithms. An important but underrated area is the uncertainty quantification (UQ) of ML. ML-based models are subject to approximation uncertainty when they are used to make predictions due to sources including but not limited to, data noise, data coverage, extrapolation, imperfect model architecture, and the stochastic training process. The goal of this paper is to clearly explain and illustrate the importance of the UQ of ML. We elucidate the differences in the basic concepts of UQ of physics-based models and data-driven ML models. Various sources of uncertainties in physical modeling and data-driven modeling are discussed, demonstrated, and compared. We also present and demonstrate a few techniques to quantify the ML prediction uncertainties, including Monte Carlo dropout, deep ensemble, Bayesian neural networks, Gaussian processes, and conformal prediction. Finally, we discuss the need for building a verification, validation, and UQ framework to establish ML credibility.

Assessing the impact of uncertainties in ice-sheet models is a major and challenging issue that needs to be faced by the ice-sheet community to provide more robust and reliable model-based projections of ice-sheet mass balance. In recent years, uncertainty quantification (UQ) has been increasingly used to characterize and explore uncertainty in ice-sheet models and improve the robustness of their projections. A typical UQ analysis involves first the (probabilistic) characterization of the sources of uncertainty followed by the propagation and sensitivity analysis of these sources of uncertainty. Previous studies concerned with UQ in ice-sheet models have generally focused on the last two steps but paid relatively little attention to the preliminary and critical step of the characterization of uncertainty. Sources of uncertainty in ice-sheet models, like uncertainties in ice-sheet geometry or surface mass balance, typically vary in space and potentially in time. For that reason, they are more adequately described as spatio(-temporal) random fields, which account naturally for spatial (and temporal) correlation. As a means of improving the characterization of the sources of uncertainties in ice-sheet models, we propose in this paper to represent them as Gaussian random fields with Matérn covariance function. The class of Matérn covariance functions provides a flexible model able to capture statistical dependence between locations with different degrees of spatial correlation or smoothness properties. Samples from a Gaussian random field with Matérn covariance function can be generated efficiently by solving a certain stochastic partial differential equation. Discretization of this stochastic partial differential equation by the finite element method results in a sparse approximation known as a Gaussian Markov random field. We solve this equation efficiently using the finite element method within the Ice-sheet and Sea-level System Model (ISSM). In addition, spatio-temporal samples can be generated by combining an autoregressive temporal model and the Matérn field. The implementation is tested on a set of synthetic experiments to verify that it captures well the desired spatial and temporal correlations. Finally, we demonstrate the interest of this sampling capability in an illustration concerned with assessing the impact of various sources of uncertainties on the Pine Island Glacier, West Antarctica. We find that both larger spatial and temporal correlations lengths will likely result in increased uncertainty in the projections.

Uncertainty quantification in a resonant nonlinear MEMS structure

Uncertainty quantification and sensitivity analysis are essential for improving the modeling and estimation of greenhouse gas emissions in livestock farming to evaluate and reduce the impact of uncertainty in input parameters to model output. The present study is a comprehensive review of the sources of uncertainty and techniques used in uncertainty analysis, quantification, and sensitivity analysis. The search process involved rigorous selection criteria and articles retrieved from the Science Direct, Google Scholar, and Scopus databases and exported to RAYYAN for further screening. This review found that identifying the sources of uncertainty, implementing quantifying uncertainty, and analyzing sensitivity are of utmost importance in accurately estimating greenhouse gas emissions. This study proposes the development of an EcoPrecision framework for enhanced precision livestock farming, and estimation of emissions, to address the uncertainties in greenhouse gas emissions and climate change mitigation.

The dynamic analysis of structures with uncertain parameters presents an attractive field of structural health monitoring in many cases of technological interest. In the dynamic analysis of hydraulic structures, such as existing dams, modeling assumptions, resulting inaccuracies, and changes in seismic loading are typically the main sources of uncertainties. Many hydraulic structures of concrete can be subjected to seismic loads. However, it is necessary to take haphazard or random phenomena as crucial considerations when assessing the security of these structures or planning new ones. This paper shows computational analysis for the characterization of the behavior of a concrete gravity dam under seismic loads, which are considered sources of uncertainties. The multi-linear regression methodology was performed and applied to evaluate the dynamic response of the considered structure. Numerous nonlinear time history analyses based on Latin Hypercube Sampling were realized to investigate the effect of uncertain parameters on the dynamic response. These analyses were applied to two types of seismic actions, the near and far earthquakes, which act on a concrete gravity dam. Then, a sensitivity analysis was used for each random variable to quantify its risk and clarify its influence on the dynamic behavior of the dam. Results divulge that for near-fault cases, major variables affecting the global sensitivity across all limit states are the Young’s modulus of soil and concrete. On the other hand, for far-fault cases, the important variables influencing the global sensitivity index include the compressive strength of concrete, Young’s modulus of soil, and cohesion.

This paper presents a computational framework for uncertainty quantification in prognostics in the context of condition-based monitoring of aerospace systems. The different sources of uncertainty and the various uncertainty quantification activities in condition-based prognostics are outlined in detail, and it is demonstrated that the Bayesian subjective approach is suitable for interpreting uncertainty in online monitoring. A state-space model-based framework for prognostics, that can rigorously account for the various sources of uncertainty, is presented. Prognostics consists of two important steps. First, the state of the system is estimated using Bayesian tracking, and then, the future states of the system are predicted until failure, thereby computing the remaining useful life of the system. The proposed framework is illustrated using the power system of a planetary rover test-bed, which is being developed and studied at NASA Ames Research Center.

Despite being a common procedure, abdominal hernia treatments still require improvement due to the number of relapses and other postoperative issues. In silico testing can be employed to predict the behavior of the complex abdominal wall and implant systems. Here, uncertainty quantification and sensitivity analysis are required in order to optimize the parameters of hernia repair models. This paper concerns the modeling of an abdominal wall and implant using the finite element method. A Gasser-Ogden-Holzapfel (GOH) material model is used for the abdominal wall and an orthotropic material model for the implant. The parameters of the GOH model and the orientation of the implant are assumed to be uncertain. Regression-based polynomial chaos expansion is used as a meta-modeling method for uncertainty propagation and global sensitivity analysis. The maximum force in the connection between the implant and native tissue is considered as the quantity of interest. A failure risk criterion is also defined and presented. It has been found that the significance of the material parameters depends on the type of implant that is analyzed. Likewise, the risk of connection failure varies considerably depending on the implant used. Models with different types of implant produce very diverse results. Moreover, these differences also appear in the global sensitivity index and the risk of connection failure. This would indicate that specific implant designs and material properties are crucial to the success of hernia repair surgery.

Silicon anode is the most promising candidate for next generation lithium ion batteries. A major drawback limiting its application is the significant volume change during lithiation-delithiation process, which may cause material pulverization and capacity degradation. A novel 3D bi-continuous nanoporous structured Si anode, consisting of porous metal scaffolds and thin Si coating layers, was proven to be an effective method to tackle this issue; however, uncertainty and non-uniformity, inherited from the fabrication process, will be inevitably introduced as important considerations for the performances of the Si anode. In this paper, uncertainty quantification (UQ) analysis is performed on the structured Si anode system to evaluate the influences of various design variables on its performances and to find the design optimization strategy. The biggest hurdle in the UQ study is the computational cost; to mitigate this challenge, a Gaussian Process based surrogate model is constructed using finite element simulation results as training data. It is found that the performances of the anode are rather sensitive to the geometric parameters, i.e. scaffold non-uniformity and Si layer thickness, whereas the mechanical properties of the materials are relatively less important. Furthermore, the optimal design is proposed to minimize the stress concentration in the Si anode.

This paper is one in a sequence of presentations that consider the problem of uncertainty quantification (UQ) in model verification and validation. The particular sub-topic considered here is uncertainty quantification in modeling. The objectives of the paper are to enumerate some of the various sources of uncertainty in models, as-built systems and experimental data, to define uncertainty and errors and differences between them, to introduce different types of comparative difference metrics that can be used for uncertainty quantification, and to present examples illustrating their uses. Particular emphasis is placed on the ability to quantify modeling uncertainty that includes model form uncertainty, i.e. an epistemic uncertainty that results from an incomplete understanding of the physics of the phenomenon being modeled, and/or undetected modeling error.

Accurate simulation of pipe transient wave is crucial for the design, reliability assessment, and defect detection of water supply systems. However, this is a difficult task since the wave propagation media in pipeline systems are often highly complex and involve a range of uncertainties. Experimental data show that key parameters such as valve closure time, wave speed, and pipe material coefficients are strongly uncertain and stochastic that may vary in a wide range. To analyze the transient behavior in such complex environments, surrogate models are built to realize the fast computation of uncertainty propagation. Three surrogate modeling methods, i.e., the polynomial‐chaos‐expansion, ordinary‐Kriging, and polynomial‐chaos‐Kriging, are tested and compared in terms of transient wave forecast accuracy. The global sensitivity is then analyzed via the Sobol index method, by which the most influential uncertainty sources on various transient signal features are identified.

Global sensitivity analysis (GSA) is useful to recognize important inputs for assigning priority and unimportant inputs for simplifying models by exploring whole distribution ranges. Meanwhile, regional sensitivity analysis (RSA) is also studied for finding the contribution of the critical region of an input, which can be viewed as the complementary of GSA. However, there is a lack of GSA and RSA research in presence of fuzzy uncertainty. Thus, a new global sensitivity index (GSI) under the fuzzy uncertainty is devoted on the credibility distribution function (CrDF), a comprehensive distribution description under the fuzzy uncertainty. The CrDF-based GSI is defined by the fuzzy expectation of the difference between the CrDF and the conditional CrDF of the output on fixing the fuzzy input over its whole distribution range, which can quantify the contribution of the fuzzy input to the output CrDF. Then, a new fuzzy RSA technique, the contribution to this CrDF based index (shortened by CCI) plot, is also proposed, and it can assess the effect of given regions of important inputs on output CrDF. Besides, mathematical properties of the CrDF based GSI and the CCI plot are discussed, and their solution are established by use of the fuzzy simulation with the same set of samples. After the accuracy of established fuzzy simulation solution for the CrDF based GSI and the CCI plot are verified by an analytical example, other examples are used to demonstrate the reasonability and applicability of proposed CrDF based GSI and CCI plot under fuzzy uncertainty.

The accurate prediction of shear wave velocity (Vs) is critical for earthquake engineering applications. However, the prediction is inevitably influenced by geotechnical variability and various sources of uncertainty. This paper investigates the effectiveness of integrating explainable machine learning (ML) model and Bayesian generalized linear model (GLM) to enhance both predictive accuracy and uncertainty quantification in Vs prediction. The study utilizes an Extreme Gradient Boosting (XGBoost) algorithm coupled with Shapley Additive Explanations (SHAPs) and partial dependency analysis to identify key geotechnical parameters influencing Vs predictions. Additionally, a Bayesian GLM is developed to explicitly account for uncertainties arising from geotechnical variability. The effectiveness and predictive performance of the proposed models were validated through comparison with real case scenarios. The results highlight the unique advantages of each model. The XGBoost model demonstrates good predictive performance, achieving high coefficient of determination (R2), index of agreement (IA), Kling–Gupta efficiency (KGE) values, and low error values while effectively explaining the impact of input parameters on Vs. In contrast, the Bayesian GLM provides probabilistic predictions with 95% credible intervals, capturing the uncertainty associated with the predictions. The integration of these two approaches creates a comprehensive framework that combines the strengths of high-accuracy ML predictions with the uncertainty quantification of Bayesian inference. This hybrid methodology offers a powerful and interpretable tool for Vs prediction, providing engineers with the confidence to make informed decisions.

Quality measures for the evaluation of machine learning architectures on the quantification of epistemic and aleatoric uncertainties in complex dynamical systems