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Carrying out a Probabilistic Tsunami Hazard Assessment (PTHA) requires a large number of simulations done at a high resolution. Statistical emulation builds a surrogate to replace the simulator and thus reduces computational costs when propagating uncertainties from the earthquake sources to the tsunami inundations. To reduce further these costs, we propose here to build emulators that exploit multiple levels of resolution and a sequential design of computer experiments. By running a few tsunami simulations at high resolution and many more simulations at lower resolutions we are able to provide realistic assessments whereas, for the same budget, using only the high resolution tsunami simulations do not provide a satisfactory outcome. As a result, PTHA can be considered with higher precision using the highest spatial resolutions, and for impacts over larger regions. We provide an illustration to the city of Cilacap in Indonesia that demonstrates the benefit of our approach.

There is currently interest in the digitalisation of metrology because technologies that can measure, analyse, and make critical decisions autonomously are beginning to emerge. The notions of metrological traceability and measurement uncertainty should be supported, following the recommendations in the Guide to the Expression of Uncertainty in Measurement (GUM). However, GUM offers no specific guidance. Here, we report on a Python package that implements algorithmic data processing using ‘uncertain numbers’, which satisfy the general criteria in GUM for an ideal format to express uncertainty. An uncertain number can represent a physical quantity that has not been determined exactly. Using uncertain numbers, measurement models can be expressed clearly and succinctly in terms of the quantities involved. The algorithms and simple data structures we use provide an example of how metrological traceability can be supported in digital systems. In particular, uncertain numbers provide a format to capture and propagate detailed information about quantities that influence a measurement along the various stages of a traceability chain. More detailed information about influence quantities can be exploited to extract more value from results for users at the end of a traceability chain.

This study investigates the robustness of orbital motion in the vicinity of the asteroid 469219 Kamo'oalewa (2016 HO3) considering the uncertainties of its mass and the solar radiation pressure. By applying the automatic domain splitting algorithm, these uncertainties are propagated and their effects on orbits with different geometries are investigated. Moreover, the bounds of the state flow are also evaluated along the propagation as an indicator of the motion sensitivity to uncertainties. An analysis of the results obtained shows that polar orbits are more robust to these uncertainties than equatorial and inclined orbits. Specifically, the solar terminator orbit is bounded within a small range and has the best robustness among all the polar orbits, thus can be used for practical mission purposes. Our studies prove that robust orbits exist even for very small bodies with weak gravity fields. Therefore, this work contributes to systematically identifying robust motions near an asteroid when uncertainties of the gravity and the SRP are simultaneously considered, addressing the challenge of real mission operations.

The key purpose of robust design and tolerancing approaches is the management of uncertainty. Against this background, it is not sur prising that there is a large overlap between the basic ideas and concepts in both fields. However, while sharing the same objective, the focus of the corresponding development phases is quite differ ent; that is (i) the determination of solutions that react insensitive, in other words robust, to n oise factors – Robust parametric design; and (ii) the limitation of the effects of manufacturing imprecision by the specification of optimal tolerances – Tolerancing. As a consequence, there also is a significant gap between both concepts. Focusing on the improvement of design solutions, robustness is often related to uncertainty of not known designs or manufacturing processes. Due to the complexity of a largely matured solution, tolerancing tasks are usually based on previously specified, key characteristics or behavior models that are supposed perfect. Therefore, an overview of robust design and tolerancing is used to highlight the deficiencies, and to formalize a new classification of tolerance analysis issues based on the type of uncertainty considered. The proposed framework is based on Dempster-Shafer evidence theory and allows to efficiently perform statistical tolerance analyses under model imprecision.

Many calculations for science or trade require the evaluation and propagation of measurement uncertainty. Although relative atomic masses (standard atomic weights) of elements in normal terrestrial materials and chemicals are widely used in science, the uncertainties associated with these values are not well understood. In this technical report, guidelines for the use of standard atomic weights are given. This use involves the derivation of a value and a standard uncertainty from a standard atomic weight, which is explained in accordance with the requirements of the Guide to the Expression of Uncertainty in Measurement. Both the use of standard atomic weights with the law of propagation of uncertainty and the Monte Carlo method are described. Furthermore, methods are provided for calculating uncertainties of relative molecular masses of substances and their mixtures. Methods are also outlined to compute material-specific atomic weights whose associated uncertainty may be smaller than the uncertainty associated with the standard atomic weights.

© 2022 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works Many traditional control solutions in urban drainage networks suffer from unmodelled nonlinear effects such as rain and wastewater infiltrating the system. These effects are challenging and often too complex to capture through physical modelling without using a high number of flow sensors. In this article, we use level sensors and design a stochastic model predictive controller by combining nominal dynamics (hydraulics) with unknown nonlinearities (hydrology) modelled as Gaussian processes. The Gaussian process model provides residual uncertainties trained via the level measurements and captures the effect of the hydrologic load and the transport dynamics in the network. To show the practical effectiveness of the approach, we present the improvement of the closed-loop control performance on an experimental laboratory setup using real rain and wastewater flow data.

This work addresses the problem of propagating uncertainty from group-wise neutron cross-sections to the results of neutronics diffusion calculations. Automatic differentiation based on dual number arithmetic was applied to uncertainty propagation in the framework of local sensitivity analysis. As an illustration, we consider a two-group diffusion problem in an infinite medium, which has a solution in a closed form. We employ automatic differentiation in conjunction with the sandwich formula for uncertainty propagation in three ways. Firstly, by evaluating the analytical expression for the multiplication factor using dual number arithmetic. Then, by solving the diffusion problem with the power iteration algorithm and the algebra of dual matrices. Finally, automatic differentiation is used to calculate the partial derivatives of the production and loss operators in the perturbation formula from the adjoint-weighted technique. The numerical solution of the diffusion problem is verified against the analytical formulas and the results of the uncertainty calculations are compared with those from the global sensitivity analysis approach. The uncertainty values obtained in this work differ from values given in the literature by less than 1?10?5.

International audience; Uncertainty propagation (UP) of the frequency response is essential for the robust design of viscoelastic damping structures. One challenge in solving this problem is enormous computation cost from the UP analysis. This paper aims to develop a novel computational effective method based on the combination of the adaptive sparse grid collocation (ASGC) method and the high dimensional model representation (HDMR) technique to evaluate the variability of the frequency response of viscoelastic damping structures. First, a well-validated layer-wise finite element method is employed to model the viscoelastic damping structures. The direct frequency response (DFR) method is utilized to calculate the response. Then, a modified adaptive strategy using expectation increments as the sampling indicator is proposed for cost-effective sparse grid construction. Lastly, high dimensional model representation (HDMR) technique is introduced to address the difficulty in moderate and high random dimensional situations. Two numerical examples are provided to assess the performances of the proposed method. Variations in constitutive parameters of viscoelastic material and thicknesses of the viscoelastic layer are considered. Numerical results show that, compared to the original high-dimensional ASGC method and Monte Carlo Simulation (MCS), the proposed method accurately predicts the variability of frequency responses and significantly improves the computational efficiency.

A new multifidelity method is developed for nonlinear orbit uncertainty propagation. This approach guarantees improved computational efficiency and limited accuracy losses compared to fully high-fidelity counterparts. The initial uncertainty is modeled as a weighted sum of Gaussian distributions whose number is adapted online to satisfy the required accuracy. As needed, univariate splitting libraries are used to split the mixture components along the direction of maximum nonlinearity. Differential Algebraic techniques are used to propagate these Gaussian kernels and compute a measure of nonlinearity required for the split decision and direction identification. Taylor expansions of the flow of the dynamics are computed using a low-fidelity dynamical model to maximize computational efficiency and corrected with selected high-fidelity samples to minimize accuracy losses. The effectiveness of the proposed method is demonstrated for different dynamical regimes combining SGP4 theory and numerical propagation as low- and high-fidelity models respectively., Comment: 24 pages, 5 figures

This paper investigates the propagation of estimation errors through a common coning, sculling, and scrolling architecture used in modern-day inertial navigation systems. Coning, sculling, and scrolling corrections often have an unaccounted for effect on the error statistics of inertial measurements used to describe the state and uncertainty propagation for position, velocity, and attitude estimates. Through the development of an error analysis for a set of coning, sculling, and scrolling algorithms, mappings of the measurement and estimation errors through the correction term are adaptively generated. Using the developed mappings, an efficient and consistent propagation of the state and uncertainty, within the multiplicative extended Kalman filter architecture, is achieved. Monte Carlo analysis is performed, and results show that the developed system has favorable attributes when compared to the traditional mechanization.

International audience; The presented adaptive modelling approach aims to jointly control the level of refinement for each of the building-blocks employed in a typical chain of finite element approximations for stochas-tically parametrized systems, namely: (i) finite error approximation of the spatial fields (ii) surro-gate modelling to interpolate quantities of interest(s) in the parameter domain and (iii) Monte-Carlo sampling of associated probability distribution(s). The control strategy seeks accurate calculation of any statistical measure of the distributions at minimum cost, given an acceptable margin of error as only tunable parameter. At each stage of the greedy-based algorithm for spatial discreti-sation, the mesh is selectively refined in the subdomains with highest contribution to the error in the desired measure. The strictly incremental complexity of the surrogate model is controlled by enforcing preponderant discretisation error integrated across the parameter domain. Finally, the number of Monte-Carlo samples is chosen such that either (a) the overall precision of the chain of approximations can be ascertained with sufficient confidence, or (b) the fact that the computational model requires further mesh refinement is statistically established. The efficiency of the proposed approach is discussed for a frequency-domain vibration structural dynamics problem with forward uncertainty propagation. Results show that locally adapted finite element solutions converge faster than those obtained using uniformly refined grids.

The performance evaluation of vapor compression and Organic Rankine Cycles relies on the employment of thermophysical libraries. The evaluation of enthalpy, for example, requires the prediction of specific heat. Thermophysical properties, in turn, depend on the state of the fluid, and thus the library is needed. The actual state of the fluid can be obtained by measuring two state properties. Typically, pressure and temperature are evaluated by means of thermocouples and pressure sensors. These measurements are affected by uncertainty, that propagates when the quantities are combined. A physical quantity calculated starting from temperature and pressure is affected by an uncertainty that is a function of the one related to the measurement of the two base quantities and of the thermophysical library employed. This can indeed propagate differently the two starting uncertainty magnifying the contribution of temperature rather than pressure. In this work the propagation of temperature and pressure uncertainty in relation to the enthalpy calculation through the CoolProp library is investigated. The procedure is applied to a number of pure refrigerants and a mixture of common use in the engineering practice. The database reported can be of help to estimate the propagation of the uncertainty in the most common engineering application.

The response up to collapse of masonry arch bridges is very complex and affected by many uncertainties. In general, accurate response predictions can be achieved using sophis-ticated numerical descriptions, requiring a significant number of parameters that need to be properly characterised. This study focuses on the sensitivity of the behaviour of masonry arch bridges with respect to a wide range of mechanical parameters considered within a de-tailed modelling approach. The aim is to investigate the effect of constitutive parameters variations on the stiffness and ultimate load capacity under vertical loading. First, advanced numerical models of masonry arches and of a masonry arch bridge are developed, where a mesoscale approach describes the actual texture of masonry. Subsequently, a surrogate kriging metamodel is constructed to replace the accurate but computationally expensive numerical descriptions, and global sensitivity analysis is performed to identify the mechani-cal parameters affecting the most the stiffness and load capacity. Uncertainty propagation is then performed on the surrogate models to estimate the probabilistic distribution of the re-sponse parameters of interest. The results provide useful information for risk assessment and management purposes, and shed light on the parameters that control the bridge behav-iour and require an accurate characterisation in terms of uncertainty.

International audience; In this paper, a model-based prognosis method where the degradation cannot be directly measured but only detectable through the drift of a model parameter is considered. This parameter drift is viewed as an unknown input, whose reconstruction allows the estimation of the degradation state. Model-based prognosis is divided into a filtering step where the current degradation state is estimated, and an uncertainty propagation step where the future degradation state is predicted. During these two steps, model uncertainty and measurement uncertainty are taken into account within the set-membership framework using interval techniques. The filtering step is performed with an interval unknown input observer for linear time-invariant discrete systems. Then, based on a set-membership constraint satisfaction methodology , interval propagation is performed to estimate the bounds that include the future degradation state until some failure threshold is reached, allowing the deduction of the interval including the remaining useful life. In order to demonstrate the efficiency of the proposed model-based prognosis methodology, the degradation of a suspension system is studied.

This paper discusses the serviceability assessment of footbridges considering the uncertainties in definition of their structural and loading parameters. Application of the Taylor Series Expansion ...

Although uncertainties such as solar radiation and material properties are generally involved in the solar receiver design process, current studies in the solar receiver field are based on deterministic models and do not incorporate these uncertainties into the design process. In this paper, based on a coupled deterministic thermal–structural model and an uncertainty analysis model, an analysis of temperature and thermal stress was conducted for a solar power tower (SPT) molten salt receiver under multi-source uncertainties to investigate the dispersions of responses. The results demonstrated that the maximum temperature inside the tube wall under multi-source uncertainties ranged from 847 K to 895 K, with an expectation of 871 K and a standard deviation of 8 K, and the maximum thermal stress ranged from 173 MPa to 245 MPa, with an expectation of 204 MPa and a standard deviation of 12 MPa, both of which had severer probabilities than the deterministic results (871 K and 204 MPa) and may cause failure in the receiver. Furthermore, the results of the global sensitivity analysis indicated that the peak incident solar flux was the most sensitive, and the specific heat of the tube material was the least sensitive to the maximum temperature and thermal stress of the tube wall. These results are beneficial to provide additional reliability and confidence in the temperature and thermal stress evaluation process of solar receiver tubes.

This paper presents an approach for probabilistic design and safety assessment of sandwich pipelines under external pressure. The methodology consists of the categorisation of sandwich pipeline collapse strength models based on interlayer adhesion conditions. The models are validated by comparing their predictions against collapse test data of sandwich pipelines. The accuracy of the strength models and their prediction uncertainty are used to select the best model in each category. Regarding interlayer adhesion categories, uncertainty propagation of models’ predictions over a wide range is assessed by the Monte Carlo simulation method. The proposed methodology is demonstrated using a case study of a sandwich pipeline with adequate probabilistic modelling of the basic random variables. Different limit states are defined for three categories of sandwich pipelines, based on which structural reliability indices are estimated. In employing the First Order Reliability Method for sensitivity analysis, the importance of basic variables of the limit states is evaluated. Later, a parametric analysis is conducted, presenting reliability variations for several design and operational scenarios of sandwich pipelines. Finally, to achieve a uniform level of structural reliability of sandwich pipelines, a few suggestions are provided, and practical partial safety factors are calculated. The results of the present analysis can provide guidance on the probabilistic design and operational safety assessment of sandwich pipelines.

ispartof: APPLIED ACOUSTICS vol:198 status: published

A comprehensive uncertainty analysis methodology has been established for the modeling of stationary neutron flux oscillations induced by fuel rods vibration in a zero-power reactor. The methodology includes uncertainty propagation and sensitivity analysis. The target event is based on an actual experimental campaign at the CROCUS zero-power reactor and corresponds to the simultaneous oscillation of 18 metallic uranium fuel rods in the periphery of the core. Both the uncertainty propagation and the sensitivity analysis commonly use a large part of the entire analysis process, from the selection of uncertain parameters to the actual code simulations. Applying a random sampling-based approach, the input parameters are sampled N times from their distribution information and used as inputs for N noise simulations using CORE SIM +. The quantity of interest (QoI) is the amplitude of the Auto-Power Spectral Density at various detector locations, which is normalized by the amplitude of the Cross-Power Spectral Density of the reference detector. Their uncertainties are determined following the 4th order Wilks’ formula for two-sided limits. Through the determination of correlations among QoI at the installed detector locations, it is demonstrated that the neutron noise near the area of oscillating fuel rods (noise source) have different behavior compared to the neutron noise further away from the noise source. The following sensitivity analyses are carried out using multiple correlation coefficients within grouped parameters. As expected from the QoI correlations, the QoIs at two different locations (near and far from the noise source) are influenced by different input parameters. Near the noise source, the QoI uncertainty is driven by the uncertainties in the position of the noise source, while the uncertainties in the nuclear data for U-235 and U-238 are the leading contributors further away from the source. This paper provides general information on how to perform the uncertainty analyses for neutron noise simulations, as well as quantitative estimates of the computational uncertainty required for the validation of the computer programs under development for the simulation of neutron noise.

The three-probe method for separating the spindle rotation error and the specimen form error is extensively described in the literature. An attractive feature is its application in in-process measurement. However, the resulting uncertainty is studied far less extensively. In this paper, an evaluation and propagation method for the uncertainty, as well as for an uncertainty reduction, is given based on the system transfer function (S-function). First, based on the Laplace transform, the measurement system model is developed and expressed by an S-function. Second, the propagation laws of input uncertainties are analytically deduced by computing the partial derivatives of the S-function of roundness. Then, the laws are numerically validated by Monte Carlo simulations. The uncertainty propagation laws show that the uncertainties propagate with varying amplification over the harmonic domain, and moreover, they enable the quantification of roundness uncertainty. Taking the roundness uncertainty as a decisive parameter, three approaches are proposed for uncertainty reduction: (1) the hybrid 3-PM, where two roundness estimates are combined by taking individual harmonic estimate with the lowest uncertainty, (2) the fusion 3-PM, where the weighted average is taken over the harmonic domain, and (3) the angle optimization, which minimizes the total roundness uncertainty by properly arranging the sensor angles. The angle optimization is applied to the conventional 3-PM, as well as to the hybrid and the fusion 3-PMs. The genetic algorithm is adopted to speed up the optimization process. Finally, practical roundness measurements are performed. The three-probe method for separating the spindle rotation error and the specimen form error is extensively described in the literature. An attractive feature is its application in in-process measurement. However, the resulting uncertainty is studied far less extensively. In this paper, an evaluation and propagation method for the uncertainty, as well as for an uncertainty reduction, is given based on the system transfer function (S-function). First, based on the Laplace transform, the measurement system model is developed and expressed by an S-function. Second, the propagation laws of input uncertainties are analytically deduced by computing the partial derivatives of the S-function of roundness. Then, the laws are numerically validated by Monte Carlo simulations. The uncertainty propagation laws show that the uncertainties propagate with varying amplification over the harmonic domain, and moreover, they enable the quantification of roundness uncertainty. Taking the roundness uncertainty as a decisive parameter, three approaches are proposed for uncertainty reduction: (1) the hybrid 3-PM, where two roundness estimates are combined by taking individual harmonic estimate with the lowest uncertainty, (2) the fusion 3-PM, where the weighted average is taken over the harmonic domain, and (3) the angle optimization, which minimizes the total roundness uncertainty by properly arranging the sensor angles. The angle optimization is applied to the conventional 3-PM, as well as to the hybrid and the fusion 3-PMs. The genetic algorithm is adopted to speed up the optimization process. Finally, practical roundness measurements are performed. ispartof: Precision Engineering vol:68 pages:139-157 status: Published online

This paper proposed a novel multi-spacecraft tracking and data association method based on the orbit uncertainty propagation. The proposed method makes full use of the dynamic information and thus the data association performance is enhanced. The proposed method is divided into three portions, i.e., the uncertainty propagation, the data association, and the orbit estimation. The second-order solutions derived for state and measurement prediction, on which to base the optimal association, are set up. The optimal association is solved by the contract network algorithm to reduce the computing cost. Finally, a second-order extended Kalman filter is designed to estimate the orbit of each spacecraft. The proposed method is successfully applied for solving a four-spacecraft tracking problem. Simulations show that all the four targets are well tracked. The method demonstrates close to 100% data association precision. The proposed method is proved to be efficient and effective to solve the multi-spacecraft tracking problem.

The upload comprises slides of the talk 'A statistical approach to the phasing of sea ice retreat and atmospheric reorganization at the onset of Dansgaard Oeschger events based on stochastic transition detection' held during the IUCLID workshop that took place from 30th September to 2nd October at the Potsdam Institute for Climate Impact Research.

Ammonia/hydrogen-fueled combustion represents a very promising solution for the futureenergy scenario. This study aims to shed light and understand the behavior of ammonia/hydrogen blends under flameless conditions. A first-of-its-kind experimental campaignwas conducted to test fuel flexibility for different ammonia/hydrogen blends in a flamelessburner, varying the air injector and the equivalence ratio. NO emissions increaseddrastically after injecting a small amount of NH3 in pure hydrogen (10% by volume). Anoptimum trade-off between NOx emission and ammonia slip was found when workingsufficiently close to stoichiometric conditions (ϕ=0.95). In general, a larger air injector(ID25) reduces the emissions, especially at ϕ=0.8. A well-stirred reactor network withexhaust recirculation was developed exchanging information with computational fluiddynamics (CFD) simulations, to model chemistry in diluted conditions. Such a simplifiedsystemwas then used in two ways: 1) to explain the experimental trends of NOx emissionsvarying the ammonia molar fraction within the fuel blend and 2) to perform an uncertaintyquantification study. A sensitivity study coupled with latin hypercube sampling (LHS) wasused to evaluate the impact of kinetic uncertainties on NOx prediction in a well-stirredreactor network model. The influence of the identified uncertainties was then tested inmore complex numerical models, such as Reynolds-averaged Navier–Stokes (RANS)simulations of the furnace. The major over-predictions of existing kinetic scheme was thenalleviated significantly, confirming the crucial role of detailed kinetic mechanisms foraccurate predictive simulations of NH3/H2 mixtures in flameless regime., 0, info:eu-repo/semantics/published

CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior CNPq - Conselho Nacional de Desenvolvimento Científico e Tecnológico Nesta tese, uma metodologia simples para encontrar bandas de atenuação robustas é apresentada. Quatro estruturas periódicas diferentes são usadas como exemplos numéricos para modelos infini-tos e finitos. As duas primeiras estão relacionadas às zonas de atenuação criadas para ondas longitudinais utilizando sistemas massa-mola e barras como células unitárias. O método da Matrix de Transferência é usado para modelar a célula unitária. Com este método, é possível obter respostas em frequência, usando um método espectral, e constantes de dispersão, resolvendo um problema de autovalor. Os parâmetros físicos e geométricos mais influentes são determinados pela realização de análises de sensibilidade através de derivadas parciais e diferenças finitas usando um modelo infinito. Para o segundo exemplo, a área de seção transversal de meia célula é considerada como uma variável estocástica representada por uma função densidade de probabilidade com propriedades de desvio específicas para uma análise probabilística. O terceiro exemplo diz respeito às bandas proibidas para ondas de flexão usando células unitárias compostas por vigas. Para este caso, o método clássico de Matriz de Transferência não pode ser usado para obter as respostas de estruturas finitas em baixa frequência devido à presença de matrizes mal condicionadas. Portanto, um método recursivo denominado Matriz de Translação, que evita a multiplicação de matrizes, é usado e a análise probabilística correspondente é realizada usando a espessura de meia célula co-mo variável aleatória. Uma análise experimental também é realizada para este caso, mas considerando o comprimento de meia célula como incerto. O último exemplo é uma treliça periódica considerada com e sem componentes inteligentes. A célula unitária desta estrutura é modelada utilizando o método de elementos finitos e pode apresentar membros passivos e ativos. No entanto, esse tipo de estrutura não possui rupturas de impedância fortes o suficiente para abrir bandas de atenuação, embora haja a presença de subestruturas repetitivas. Em virtude disto, oito cenários são investigados considerando a introdução de massa concentrada em articulações e atuadores piezoelétricos em circuito shunt ressonante que são considerados estocásticos para casos específicos. Para cada modelo estrutural, uma Simulação de Monte Carlo com amostragem por Hipercubo Latino é realizada, as diferenças entre as zonas de atenuação incertas correspondentes aos modelos finitos e infinitos são expostas e a relação com modos localizados é esclarecida. Os resultados levam a concluir que os modelos finitos possuem uma região de atenuação maior do que as regiões equivalentes apresentadas por modelos infinitos considerando parâmetros estocásticos. Em outras palavras, as incertezas entre células vizinhas se compensam e as estruturas periódicas finitas são naturalmente mais robustas. Finalmente, o efeito do aumento do nível de incerteza, variando um coeficiente estocástico, é analisado e o conceito de banda de atenuação robusta é apresentado. In this thesis, a simple methodology to find robust bandgaps is presented. Four different periodic structures are used as numerical examples for infinite and finite models. The first two are related to attenuation zones created for longitudinal waves using spring-mass and stepped rod unit cells. The Transfer Matrix method is used to model the unit cell. With this method, it is possible to obtain the frequency responses, using a spectral method, and dispersion constants, solving an eigenvalue problem. The most influential physical and geometrical parameters are determined by performing partial derivative and finite difference sensitivity analysis through an infinite model. Therein, for the second example, the cross-section area of half-cell is considered as a stochastic variable represented by a probability density function with specific deviation properties for a probabilistic analysis. The third example concerns the bandgaps for flexural waves using stepped beams unit cells. For this case, the classical Transfer Matrix method cannot be used to obtain finite structures response in low frequency because of the presence of ill-conditioned matrices. Therefore, a recursive method termed Translation Matrix, which avoids matrix multiplication, is used and the corresponding probabilistic analysis is performed using the half-cell thickness as a random variable. An experimental analysis is also performed for this case, but considering half-cell length as uncertain. The last example is a periodic truss that is considered with and without smart components. The unit cell of this lattice structure can present passive and active members. As long as the type of unit cell is more complex, the finite element method is used. However, this kind of structure does not have impedance mismatches strong enough to open bandgaps although the presence of repetitive sub-structures. In virtue of this, eight scenarios are investigated considering the introduction of concentrated mass on joints and piezoelectric actuators in resonant shunt circuit which are considered as stochastic for specific cases. For each structure model, a Monte Carlo Simulation with Latin Hyper-cube sampling is carried out, the distinctions between the corresponding uncertain attenuation zones for finite and infinite models are exposed and the relation with localized modes is clarified. These results lead to conclude that the finite models present a larger stop zone considering stochastic parameters than infinite models. In other words, the uncertainties between neighbor cells compensate each other and the finite structures are naturally more robust. Finally, the effect of increasing the uncertainty level, by varying a stochastic coefficient, is analyzed and the concept of robust band gap is presented. Tese (Doutorado)

When using a chain of numerical models in a stochastic simulation, the distribution of the observed output depends on both the input parameter uncertainty and the errors of the individual models in the chain. In this work, the propagation of model uncertainty is studied in a simple one-dimensional heat-transfer system. The errors in temperature are found to depend on the heat flux coupling scenario and on the type of the input parameter distributions. The radiation heat flow boundary condition limits the error propagation by compensating the gas temperature errors through enhanced heat losses. Model biases were found to be detrimental to the accuracy of the predicted probabilities of exceeding safety criteria. Finally, corrections to the predicted distribution moments are proposed and tested, showing that the error contributions can be effectively eliminated from the observed distributions if the properties of the individual models are well known.

In this paper, we consider the computational model of a dynamic aerospace system and address the issues posed by the NASA Langley Uncertainty Quantification Challenge on Optimization Under Uncertainty, which comprises six tasks. Subproblem A deals with the model calibration and (aleatory and epistemic) uncertainty quantification of a subsystem by means of a limited number of observations. A simple, two-step approach based on Maximum Likelihood Estimation (MLE) is proposed to address this task. Subproblem B requires the identification and ranking of those (epistemic) parameters that are more effective in improving the predictive ability of the computational model of the subsystem. Two approaches are compared: the first is based on a sensitivity analysis within a factor prioritization setting, whereas the second employs the Energy Score (ES) as a multivariate generalization of the Continuous Rank Predictive Score (CRPS). Since the output of the subsystem is a function of time, both subproblems are addressed in the space defined by the orthonormal bases resulting from a Singular Value Decomposition (SVD) of the subsystem observations. Subproblem C requires identifying the (epistemic) reliability (resp., failure probability) bounds of a given system design. The issue is addressed by an efficient combination of: (i) Monte Carlo Simulation (MCS) to propagate the aleatory uncertainty described by probability distributions; (ii) Genetic Algorithms (GAs) to solve the optimization problems related to the propagation of epistemic uncertainty by interval analysis; and (iii) fast-running Artificial Neural Networks (ANNs) to reduce the computational time related to the repeated model evaluations. In Subproblem D, system reliability is improved by identifying a new design point within an iterative robust optimization framework. In Subproblem E both the uncertainty model and the design obtained are tuned using additional data. Finally, a risk-based design is carried out in Subproblem F by neglecting “outliers” (i.e., less likely values of some epistemic parameters) in the design optimization.

Confidence intervals of divergence times and branch lengths do not reflect uncertainty about their clades or about the prior distributions and other model assumptions on which they are based. Uncertainty about the clade may be propagated to a confidence interval by multiplying its confidence level by the bootstrap proportion of its clade or by another probability that the clade is correct. (If the confidence level is 95% and the bootstrap proportion is 90%, then the uncertainty-adjusted confidence level is (0.95)(0.90) = 86%.) Uncertainty about the model can be propagated to the confidence interval by reporting the union of the confidence intervals from all the plausible models. Unless there is no overlap between the confidence intervals, that results in an uncertainty-adjusted interval that has as its lower and upper limits the most extreme limits of the models. The proposed methods of uncertainty quantification may be used together.

Resumen En la identificación de sistemas mecánicos la atención se ha concentrado en formular y evaluar métodos robustos frente a la presencia de mediciones contaminadas con “ruido”, de modo que se relega el estudio de la influencia de la incertidumbre experimental en los parámetros identificados del sistema. Esta investigación presenta una formulación general para la estimación de los errores vinculados con la identificación de las matrices de inercia, rigidez y amortiguación viscosa de sistemas mecánicos linealizados. Se realiza la propagación de las incertidumbres experimentales a través de la función de respuesta en frecuencia, de lo que se obtiene una expresión genérica para el cálculo de su incertidumbre, luego de recurrir a propiedades del producto de Kronecker y del cálculo matricial. Se ilustra la formulación mediante la caracterización experimental de un sistema mecánico simple con el empleo de dos métodos de identificación: mínimos cuadrados y variable instrumental. La validación de la metodología se realiza mediante comparación de los resultados obtenidos con las desviaciones estándares de las muestras disponibles de cada parámetro identificado. La comparación revela coincidencia en orden de magnitud para la mayoría de las incertidumbres de los parámetros estimados, lo que confirma la consistencia de la formulación presentada para la propagación de las incertidumbres experimentales de las mediciones en la identificación de sistemas. Abstract In the parameter identification of mechanical systems, the accuracy on the parameter estimates is limited since they are obtained by processing the excitation and response system measurements which are inherently linked to experimental errors. A general formulation to estimate the un- certainty on the estimated mass, stiffness and damping matrices for linear mechanical systems is presented in this article. Pursuing applicability, the proposed methodology is formulated as an extension of the accepted practice to determine uncertainty propagation for multidimensional measurand. The approach can be applied to identification of linear mechanical systems in frequency domain, independently of the algorithm considered for estimating the system parameters. The limitations of the proposed formulation are also discussed and an experimental example is provided to illustrate the suggested methodology by means of two identification methods: ordinary least squares and instrumental variable methods. The comparison of parameters’ variability, obtained from the propagation of random uncertainties, with the one generated by direct computation, i.e. from a sample of estimates of parameters, reveals the matching orders of magnitude for most of the uncertainties of the parameter estimates, confirming the consistency of the formulation in order to propagate random and systematic measurement uncertainties in the identification of the system parameters.

Reliable 3D modelling of underground hydrocarbon reservoirs is a challenging task due to the complexity of the underground geological formations and to the availability of different types of data that are typically affected by uncertainties. In the case of geologically complex depositional environments, such as fractured hydrocarbon reservoirs, the uncertainties involved in the modelling process demand accurate analysis and quantification in order to provide a reliable confidence range of volumetric estimations. In the present work, we used a 3D model of a fractured carbonate reservoir and populated it with different lithological and petrophysical properties. The available dataset also included a discrete fracture network (DFN) property that was used to model the fracture distribution. Uncertainties affecting lithological facies, their geometry and absolute positions (related to the fault system), fracture distribution and petrophysical properties were accounted for. We included all different types of uncertainties in an automated approach using tools available in today’s modelling software packages and combining all the uncertain input parameters in a series of statistically representative geological realizations. In particular, we defined a specific workflow for the definition of the absolute permeability according to an equivalent, single porosity approach, taking into account the contribution of both the matrix and the fracture system. The results of the analyses were transferred into a 3D numerical fluid-dynamic simulator to evaluate the propagation of the uncertainties associated to the input data down to the final results, and to assess the dynamic response of the reservoir following a selected development plan. The “integrated approach” presented in this paper can be useful for all technicians involved in the construction and validation of 3D numerical models of hydrocarbon-bearing reservoirs and can potentially become part of the educational training for young geoscientists and engineers, since an integrated and well-constructed workflow is the backbone of any reservoir study.

The neutron irradiation-induced mechanical property change is a major challenge for nuclear materials. For a Pressurized Water Reactor (PWR), neutron irradiation embrittlement of the reactor pressure vessel is one of the most important issues that determine the whole nuclear power plant lifetime. The present work focuses thus on the uncertainty assessment for the neutron irradiation displacement damage of a PWR vessel. The uncertainties of neutron flux, nuclear data, and atomic displacement models are propagated to Displacement per Atom (DPA) rates with a special emphasis on the importance of correlation matrices. In addition to the uncertainty propagated from the threshold displacement energy, the total uncertainty of damage energy rate is about 10% (at 1σ), whereas the uncertainty is largely underestimated if the correlations of damage cross section and neutron flux are not considered. Apart from the complete uncertainty propagation shown in this paper, combining the damage energy rate uncertainty and the displacement threshold energy uncertainty is recommended for estimating the calculated DPA rate uncertainty. Besides the uncertainty, the biases induced by the model defects are preliminarily estimated.

The long‐term health effects of air pollution are often estimated using a spatio‐temporal ecological areal unit study, but this design leads to the following statistical challenges: (1) how to estimate spatially representative pollution concentrations for each areal unit; (2) how to allow for the uncertainty in these estimated concentrations when estimating their health effects; and (3) how to simultaneously estimate the joint effects of multiple correlated pollutants. This article proposes a novel 2‐stage Bayesian hierarchical model for addressing these 3 challenges, with inference based on Markov chain Monte Carlo simulation. The first stage is a multivariate spatio‐temporal fusion model for predicting areal level average concentrations of multiple pollutants from both monitored and modelled pollution data. The second stage is a spatio‐temporal model for estimating the health impact of multiple correlated pollutants simultaneously, which accounts for the uncertainty in the estimated pollution concentrations. The novel methodology is motivated by a new study of the impact of both particulate matter and nitrogen dioxide concentrations on respiratory hospital admissions in Scotland between 2007 and 2011, and the results suggest that both pollutants exhibit substantial and independent health effects.

International audience; Quantitative risk analysis (QRA) is a fundamental part of the decision-making process when it comes to the safety of people and the environment. However, due to the uncertainty involved, the credibility of risk assessment results is still a major issue. This paper aims to explore the most commonly used approaches to quantify uncertainty in risk analysis: interval analysis, fuzzy theory, probability theory, evidence theory, and the mixed probabilistic-fuzzy approach. These approaches are used to characterize uncertainty in model inputs obtained from different sources, such as statistical data and expert judgments, and to which different types of uncertainty can be attached. These uncertainty characterizations are then propagated through the model to obtain the corresponding representation of uncertainty for the model outputs. The paper presents the application of these quantification approaches to a loss of containment scenario (LOC), representing one of the most likely situations to occur in industry. The overall aim is to study the effects of uncertainty and compare the different approaches. Indeed, the uncertainty quantification approaches presented can lead to different representations of uncertainty in the outputs and hence to different decisions. The use of an inappropriate approach in an inappropriate place may lead to under or overestimation of risk and subsequently to a bad decision.

International audience; Being highly insulated, low-energy buildings are very sensitive to variable solar and internal gains. In this context, some modelling assumptions frequently used in simplified building energy simulation tools might be called into question. While higher insulation levels reduce the influence of heat transmission through opaque walls, absorption of solar and internal gains at inner wall surfaces, and indoor superficial heat transfers, become concerning. The convective and long-wave radiative heat transfer models are investigated in COMFIE, a dynamic energy simulation platform. More detailed internal heat transfer models are developed by decoupling convective and long-wave radiative heat transfers and using time-dependent coefficients. Furthermore, an empirical validation process on both simplified and detailed models is carried out using measurements from a full-scale experimental concrete passive house, addressing the model uncertainty vs. complexity issue.

The multivariate log-normal distribution is used by many authors and statistical uncertainty propagation programs for inherently positive quantities. Sometimes it is claimed that the log-normal distribution results from the maximum entropy principle, if only means, covariances and inherent positiveness of quantities are known or assumed to be known. In this article we show that this is not true. Assuming a constant prior distribution, the maximum entropy distribution is in fact a truncated multivariate normal distribution – whenever it exists. However, its practical application to multidimensional cases is hindered by lack of a method to compute its location and scale parameters from means and covariances. Therefore, regardless of its theoretical disadvantage, use of other distributions seems to be a practical necessity.

This article deals with the problem of room categorization, i.e. the classification of a room as being a bathroom, kitchen, living-room, bedroom, etc., by an autonomous robot operating in home environments. For that, we propose a room categorization system based on a Bayesian probabilistic framework that combines object detections and its semantics. For detecting objects we resort to a state-of-the-art CNN, Mask R-CNN, while the meaning or semantics of those detections is provided by an ontology. Such an ontology encodes the relations between object and room categories, that is, in which room types the different object categories are typically found (toilets in bathrooms, microwaves in kitchens, etc.). The Bayesian framework is in charge of fusing both sources of information and providing a probability distribution over the set of categories the room can belong to. The proposed system has been evaluated in houses from the Robot@Home dataset, validating its effectiveness under real-world conditions.

Under the performance based earthquake engineering (PBEE) philosophy, the design of structures to resist collapse requires meeting a target level of collapse prevention. Therefore, the quantification of the collapse capacity of a structure is regarded as an essential step to develop robust designs that can ensure safety under extreme earthquake scenarios. Although, in the recent two decades, tremendous progress has been achieved in the field of computational analysis of deteriorating structures, the accurate prediction of collapse capacity remains a topical issue because current methods used for predicting collapse do not correlate to the exact occurrence of dynamic instability in the structure. In the present study, a new physics-based collapse criterion is proposed. It uses power (energy-rates) to predict seismic collapse capacity of structures. The development of the criterion stems from the principles of Lyapunov stability and dissipative dynamical systems. A series of validated collapse simulation models are developed to illustrate the applicability of this criterion to both vertical gravity load and sidesway collapse mechanisms. Furthermore, a dynamical systems theory algorithm is developed to identify the exact occurrence of dynamic instability. The developed power-based collapse criterion is then optimised by comparing its collapse predictions to those derived from the dynamical systems theory algorithm. Finally, the refined power-criterion is then used to evaluate the collapse risk in realistic RC frame buildings designed to meet existing codes’ requirements. The collapse risk estimates are compared to those derived from the existing techniques. It was found that the proposed criterion can serve as a leading indicator of collapse and can potentially result in economic and safe designs.

Presentation on the comparison of errors-in-variables and marginalised errors-in-variables harmonisation methods given by R. Quast during the FIDUCEO science meeting at NPL in January 2019. This presentation supplements the journal article: Giering, R.; Quast, R.; Mittaz, J.P.D.; Hunt, S.E.; Harris, P.M.; Woolliams, E.R.; Merchant, C.J. A Novel Framework to Harmonise Satellite Data Series for Climate Applications. Remote Sens. 2019, 11, 1002. doi:10.3390/rs11091002., {"references":["Giering, R.; Quast, R.; Mittaz, J.P.D.; Hunt, S.E.; Harris, P.M.; Woolliams, E.R.; Merchant, C.J. A Novel Framework to Harmonise Satellite Data Series for Climate Applications. Remote Sens. 2019, 11, 1002"]}

In air pollution studies a key issue concerns the change of support: pollutant concentrations are continuous phenomena in space but their measurements are typically available at a finite number of point-referenced monitoring stations or result from numerical models. When linking exposure to health outcomes, the latter are usually available at administrative level, hence on an irregular lattice, providing challenges in terms of data misalignment. In this paper we tackle the change of support problem for air pollution and health studies through a two-stage Bayesian approach; in the first stage our model estimates the air pollution concentration at the area level and then in the second stage it links the exposure to the health outcome, accounting for the uncertainty on the exposure estimates. We show through an extensive and realistic simulation that our model is able to predict the concentration accurately at the administrative level as well as estimate the association between exposure and health outcome. We use the Integrated Nested Laplace Approximation, coupled with the Stochastic Partial Differential Equation method for model implementation. Finally we apply the proposed model to evaluate the effect of NO 2 concentration on hospital admissions for respiratory diseases in the Piemonte region (Italy). We found that the upscaling method and the approach used to propagate uncertainty from the first to the second stage have an impact on the posterior distribution of the relative risk. Moreover, we found a significant increased risk of 1.6% and 1.8% associated with an increase of 10 μ g ∕ m 3 in NO 2 concentration.

Made available in DSpace on 2021-06-25T10:56:26Z (GMT). No. of bitstreams: 0 Previous issue date: 2021-06-09 Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) A good estimate of the speed of leak noise propagation is necessary to pinpoint the location of a leak using acoustic correlators. Models currently exist for this purpose, but they do not consider uncertainties in the pipe geometry and the properties of the pipe and soil. Using the fact that leak noise propagates as a predominantly fluid-borne wave, this paper develops a stochastic model of the speed of leak noise propagation in plastic water distribution pipes that can account for these uncertainties. The model provides confidence limits for the estimate of this wave speed. It is based on the mean and standard deviation of the pipe geometry as well as the pipe and soil material properties, which have strong influence on the speed at which the leak noise propagates in the pipe. Numerical examples, using parameters from water supply systems found in the field, in which the pipe is made from Medium-Density Polyethylene (MDPE) and Polyvinyl Chloride (PVC) are presented to validate the model. Monte Carlo simulations for both in-air and buried pipes are presented to check the 99.7% confidence interval. To verify that the predictions from the stochastic models give realistic results, they are compared with some measurements from different sites, in which nominal properties and tolerances for the pipe and soil properties are assumed. Department of Mechanical Engineering UNESP-FEIS Dokuz Eylül University Department of Mechanical Engineering Institute of Sound and Vibration Research University of Southampton Faculty of Science and Engineering UNESP-FCE Department of Mechanical Engineering UNESP-FEB Department of Mechanical Engineering UNESP-FEIS Faculty of Science and Engineering UNESP-FCE Department of Mechanical Engineering UNESP-FEB FAPESP: 2018/25360-3 CAPES: 88887.374001/2019-00

International audience; An objective of satellite remote sensing is to predict or characterize the land cover change (LCC) over time. Sometimes we are capable of describing the changes of land cover with a probability distribution. However, we need sufficient knowledge about the natural variability of these changes, which is not always possible. In general, uncertainties can be subdivided into aleatory and epistemic. The main problem is that classical probability theory does not make a clear distinction between aleatory and epistemic uncertainties in the way they are represented, i.e., both of them are described with a probability distribution. The aim of this paper is to propagate the aleatory and epistemic uncertainty associated with both input parameters (features extracted from satellite image object) and model structure of LCC prediction process using belief function theory. This will help reducing in a significant way the uncertainty about future changes of land cover. In this study, the changes prediction of land cover in Cairo region, Egypt for next 16 years (2030) is anticipated using multi-temporal Landsat TM5 satellite images in 1987 and 2014. The LCC prediction model results indicated that 15% of the agriculture and 6.5% of the desert will be urbanized in 2030. We conclude that our method based on belief function theory has a potential to reduce uncertainty and improve the prediction accuracy and is applicable in LCC analysis.

This study illustrates a procedure conducive to a preliminary risk analysis of overpressure development in sedimentary basins characterized by alternating depositional events of sandstone and shale layers. The approach rests on two key elements: (1) forward modeling of fluid flow and compaction, and (2) application of a model-complexity reduction technique based on a generalized polynomial chaos expansion (gPCE). The forward model considers a one-dimensional vertical compaction processes. The gPCE model is then used in an inverse modeling context to obtain efficient model parameter estimation and uncertainty quantification. The methodology is applied to two field settings considered in previous literature works, i.e. the Venture Field (Scotian Shelf, Canada) and the Navarin Basin (Bering Sea, Alaska, USA), relying on available porosity and pressure information for model calibration. It is found that the best result is obtained when porosity and pressure data are considered jointly in the model calibration procedure. Uncertainty propagation from unknown input parameters to model outputs, such as pore pressure vertical distribution, is investigated and quantified. This modeling strategy enables one to quantify the relative importance of key phenomena governing the feedback between sediment compaction and fluid flow processes and driving the buildup of fluid overpressure in stratified sedimentary basins characterized by the presence of low-permeability layers. The results here illustrated (1) allow for diagnosis of the critical role played by the parameters of quantitative formulations linking porosity and permeability in compacted shales and (2) provide an explicit and detailed quantification of the effects of their uncertainty in field settings.

Engineering and applied sciences use models of increasing complexity to simulate the behavior of manufactured and physical systems. Propagation of uncertainties from the input to a response quantity of interest through such models may become intractable in cases when a single simulation is time demanding. Particularly challenging is the reliability analysis of systems represented by computationally costly models, because of the large number of model evaluations that are typically required to estimate small probabilities of failure. In this paper, we demonstrate the potential of a newly emerged meta-modeling technique known as low-rank tensor approximations to address this limitation. This technique is especially promising for high-dimensional problems because: (i) the number of unknowns in the generic functional form of the meta-model grows only linearly with the input dimension and (ii) such approximations can be constructed by relying on a series of minimization problems of small size independent of the input dimension. In example applications involving finite-element models pertinent to structural mechanics and heat conduction, low-rank tensor approximations built with polynomial bases are found to outperform the popular sparse polynomial chaos expansions in the estimation of tail probabilities when small experimental designs are used. It should be emphasized that contrary to methods particularly targeted to reliability analysis, the meta-modeling approach also provides a full probabilistic description of the model response, which can be used to estimate any statistical measure of interest.

The LA-ICP-MS U-(Th-)Pb geochronology international community has defined new standards for the determination of U-(Th-)Pb ages. A new workflow defines the appropriate propagation of uncertainties for these data, identifying random and systematic components. Only data with uncertainties relating to random error should be used in weighted mean calculations of population ages; uncertainty components for systematic errors are propagated after this stage, preventing their erroneous reduction. Following this improved uncertainty propagation protocol, data can be compared at different uncertainty levels to better resolve age differences. New reference values for commonly used zircon, monazite and titanite reference materials are defined (based on ID-TIMS) after removing corrections for common lead and the effects of excess 230Th. These values more accurately reflect the material sampled during the determination of calibration factors by LA-ICP-MS analysis. Recommendations are made to graphically represent data only with uncertainty ellipses at 2s and to submit or cite validation data with sample data when submitting data for publication. New data-reporting standards are defined to help improve the peer-review process. With these improvements, LA-ICP-MS U-(Th-)Pb data can be considered more robust, accurate, better documented and quantified, directly contributing to their improved scientific interpretation. La communauté internationale de la géochronologie LA-ICP-MS U-(Th-)Pb a défini les nouvelles normes pour la détermination des âges U-(Th-)Pb. Un nouveau flux de travail définit la propagation adéquate des incertitudes pour ces données, en identifiant les composants aléatoires et systématiques. Seules les données avec des incertitudes relatives à l'erreur aléatoire devraient être utilisées dans les calculs des moyennes pondérées des âges de la population; les composantes de l'incertitude pour les erreurs systématiques sont propagées après cette étape, empêchant leur réduction erronée. En suivant ce protocole amélioré pour la propagation de l'incertitude, les données peuvent être comparées à différents niveaux d'incertitude pour mieux résoudre les différences d’âge. Les nouvelles valeurs pour les matériaux de référence zircon, monazite et titanite sont définies (basée sur ID-TIMS) après les corrections du plomb commun et les effets de l'excès en 230Th. Ces valeurs reflètent plus fidèlement le matériau échantillonné lors de la détermination des facteurs d’étalonnage par analyse LA-ICP-MS. Des recommandations sont faites pour représenter graphiquement des données avec seulement des ellipses d'incertitude à 2s et pour soumettre ou pour citer des données de validation avec les données de l’échantillon lors de la soumission des données pour publication. Les nouvelles normes de déclaration des données sont définies pour améliorer le processus d'évaluation par les pairs. Grâce à ces améliorations, les données LA-ICP-MS U-(Th)-Pb peuvent être considérés comme plus solides, exactes, mieux documentées et quantifiées, contribuant ainsi à une meilleure interprétation scientifique.

The object of the present study is to investigate the influence of damping uncertainty and statistical correlation on the dynamic response of structures with random damping parameters in the neighbourhood of a resonant frequency. A Non-Linear Statistical model (NLSM) is successfully demonstrated to predict the probabilistic response of an industrial building structure with correlated random damping. A practical computational technique to generate first and second-order sensitivity derivatives is presented and the validity of the predicted statistical moments is checked by traditional Monte Carlo simulation. Simulation results show the effectiveness of the NLSM to estimate uncertainty propagation in structural dynamics. In addition, it is demonstrated that the uncertainty in damping indeed influences the system response with the effects being more pronounced for lightly damped structures, higher variability and higher statistical correlation of damping parameters.

The paper shows the application of the most recent sensitivity techniques implemented in Serpent-2 in order to propagate the uncertainty from the nuclear data to the macroscopic, homogenised cross sections of the ALFRED reactor, which is then simulated with the multi-physics code FRENETIC. The main results are encouraging and define a possible methodology to propagate the nuclear data uncertainties to the main macroscopic parameters computed with FRENETIC, in order to perform thorough safety analyses for the ALFRED reactor.

Several sources of bias are involved at each stage of a quantitative precipitation estimation process because weather radars measure precipitation amounts indirectly. Conventional methods compare the relative uncertainties between different stages of the process but seldom present the total uncertainty. Therefore, the objectives of this study were as follows: (1) to quantify the uncertainty at each stage of the process and in total, (2) to elucidate the ratio of the uncertainty at each stage in terms of the total uncertainty, and (3) to explain the uncertainty propagation process at each stage. This study proposed novel application of three methods (maximum entropy method, uncertainty Delta method, and modified-fractional uncertainty method) to determine the total uncertainty, level of uncertainty increase, and percentage of uncertainty at each stage. Based on data from 18 precipitation events that occurred over the Korean Peninsula, the applicability of the three methods was tested using a radar precipitation estimation process that comprised two quality control algorithms, two precipitation estimation methods, and two post-processing precipitation bias correction methods. Results indicated that the final uncertainty of each method was reduced in comparison with the initial uncertainty, and that the uncertainty was different at each stage depending on the method applied.