Global sensitivity analysis approaches applied to parameter selection for numerical model-updating of structures

Purpose: In particle therapy, treatment planning and evaluation are frequently based on biological models to estimate the relative biological effectiveness (RBE) or the equivalent dose in 2 Gy fractions (EQD2). In the context of the linear-quadratic model, these quantities depend on biological parameters (α, β) for ions as well as for the reference radiation and on the dose per fraction. The needed biological parameters as well as their dependency on ion species and ion energy typically are subject to large (relative) uncertainties of up to 20–40% or even more. Therefore it is necessary to estimate the resulting uncertainties in e.g. RBE or EQD2 caused by the uncertainties of the relevant input parameters. Methods: We use a variance-based sensitivity analysis (SA) approach, in which uncertainties in input parameters are modeled by random number distributions. The evaluated function is executed 10{sup 4} to 10{sup 6} times, each run with a different set of input parameters, randomly varied according to their assigned distribution. The sensitivity S is a variance-based ranking (from S = 0, no impact, to S = 1, only influential part) of the impact of input uncertainties. The SA approach is implemented for carbon ion treatment plans on 3D patient data,more » providing information about variations (and their origin) in RBE and EQD2. Results: The quantification enables 3D sensitivity maps, showing dependencies of RBE and EQD2 on different input uncertainties. The high number of runs allows displaying the interplay between different input uncertainties. The SA identifies input parameter combinations which result in extreme deviations of the result and the input parameter for which an uncertainty reduction is the most rewarding. Conclusion: The presented variance-based SA provides advantageous properties in terms of visualization and quantification of (biological) uncertainties and their impact. The method is very flexible, model independent, and enables a broad assessment of uncertainties. Supported by DFG grant WI 3745/1-1 and DFG cluster of excellence: Munich-Centre for Advanced Photonics.« less

In this paper we present a comparison between a set of benchmark centrifuge models of a jointed beam and the predictions of two numerical models: fast Lagrangian analysis of continua (FLAC) and discontinuous deformation analysis (DDA). The primary objective of this paper is a comparison between the measured deformation profiles and thrust evolution to predictions of the numerical methods employed. A secondary objective is an attempt to clarify the issue of compressive arch geometry which is still in controversy among researchers.It is found that both FLAC and DDA result in insufficiently accurate predictions to the measured displacements. The mode of deformation is only partially captured and is dependent on the aspect ratio of the individual blocks which made up the beam. It is shown that the accuracy of the predicted displacements is a function of the assigned interface stiffness. The thrust predicted by both methods is found to be considerably lower than that measured in the model; however, the linear evolution of thrust and equilibrium conditions are correctly captured.The geometry of the compressive arch as predicted by FLAC compares extremely well with the data measured in the physical model. Based on the FLAC analysis it is found that for a beam composed of equidimensional blocks the thickness of the compressive arch varies from 0.8t at the abutment interface to the entire beam thickness (1t) at a distance of a half block width from the abutment face, extending across the interface separating the block and its neighbour, and attains a value of 0.5t at the beam mid span. Copyright © 2006 John Wiley & Sons, Ltd.

Uncertainty and sensitivity analysis of cooling and heating loads for building energy planning

This paper focuses on the application of the variance-based global sensitivity analysis for a topological derivative method in order to solve a stochastic nonlinear time-dependent magnetoquasi-static interface problem. To illustrate the approach a permanent magnet (PM) synchronous machine has been considered. Our key objective is to provide a robust design of the rotor poles and of the tooth base in a stator for the reduction of the torque ripple and electromagnetic losses, while taking material uncertainties into account. Input variations of material parameters are modeled using the polynomial chaos expansion technique, which is incorporated into the stochastic collocation method in order to provide a response surface model. Additionally, we can benefit from the variance-based sensitivity analysis. This allows us to reduce the dimensionality of the stochastic optimization problems, described by the random-dependent cost functional. Finally, to validate our approach, we provide the 2-D simulations and analysis, which confirm the usefulness of the proposed method and yield a novel topology of a PM synchronous machine.

Modeling green recycled aggregate concrete using machine learning and variance-based sensitivity analysis

Simulation of fate and transport mechanisms in the porous systems from contaminant transport models are affected by uncertainty associated with input model parameters. Sensitivity analysis (SA) provides tools to quantify the sources of uncertainty to the variations in the model output metrics. To quantify the uncertainty associated with physical non-equilibrium contaminant transport model, global SA was conducted for the problem mimicking reactive transport in the saturated soil column conditions. Five global SA methods, namely Morris, RSA (Regionalized Sensitivity Analysis), Sobol, FAST (Fourier Amplitude Sensitivity Test), and PAWN, were tested based on the temporal moments of contaminant concentrations for two output metrics: zeroth temporal moment (ZTM) and mean residence time (MRT). The ranking order of ten input model parameters from global SA methods for two output metrics was compared. Morris SA implied that the ZTM at outlet of the soil column is highly sensitive to sorption distribution coefficient in the mobile and immobile regions and less sensitive to dispersion coefficient and degradation rate constant in the immobile region. The mass-transfer coefficient showed highest non-linear interactions with other flow and transport parameters based on the highest value of standard deviation of elementary effects (EEs) for ZTM output metric. The sorption distribution coefficient in the mobile region and mass-transfer coefficient showed highest sensitivity and non-linear effect toward MRT based on the Morris method. The comparison of global SA methods revealed that the top two sensitive parameters affecting ZTM and MRT were the same from all the considered methods. However, large difference in the ranking order of bottom three sensitive parameters was observed. The sorption distribution coefficient of mobile region and mass-transfer coefficient were observed as the most sensitive parameters affecting ZTM and MRT based on the comparison of all five global SA methods. Overall results suggest that the non-linear contaminant transport model should be examined based on multiple sensitivity output metrics via a multi-model approach. The multi-model global SA approach implemented in this study highlighted its significance in quantifying the interplay of non-linear model parameters.

ABSTRACTPROSAIL is a combination of the leaf optical properties spectra (PROSPECT) model and the scattering by arbitrarily inclined leaves (SAIL) canopy bidirectional reflectance model. When modelling forest canopy reflectance using the PROSAIL radiative transfer model, the sensitivities of parameters can affect the modelling accuracy. Traditionally, sensitivities have been assessed using local sensitivity analysis (LSA); however, drawbacks to this approach include a lack of consideration for coupled effects between different parameters. In this study, parameter sensitivities in the PROSAIL model were calculated using two global sensitivity analysis (GSA) methods (the Extended Fourier Amplitude Sensitivity Test (EFAST) method and the Morris method), field measurements, and Landsat 5 Thematic Mapper (TM) data for a Moso bamboo forest. The results of GSA were compared with those of LSA in order to identify the key parameters impacting the Moso bamboo forest canopy reflectance, and to provide a reference for model optimization and vegetation canopy inversion improvement. The results showed that: (1) the sensitivities of six major input parameters of the PROSAIL model were generally consistent with the sorting orders of the two GSA methods, but were not in accordance with those from the LSA method, especially in the mid-infrared band; (2) coupled effects among parameters acting on reflectance simulation in visible light bands were greater than those in infrared bands; (3) the simulated canopy reflectance was evaluated using Landsat 5 TM data, and the results simulated based on LSA analysis showed higher error than those based on GSA analysis, because the LSA method ignored the influence of some parameters on canopy reflectance, e.g. leaf mesophyll structure (N), average leaf angle (ALA), leaf water content (Cw), and leaf dry matter content (Cm). However, GSA was able to fully consider the coupled effects among parameters, and thus identified the sensitive parameters impacting on reflectance more accurately.

Copula-based methods for global sensitivity analysis with correlated random variables and stochastic processes under incomplete probability information

Improved understanding of dynamic hydrological performance of green roof (GR) design parameters towards different model responses is important for maximizing its target design goals at the unit-scale. Replication of an optimally designed GR unit at the catchment-scale significantly contributes to achieving its target design goals (i.e., surface runoff reduction, urban flood reduction, peak flow control, etc.). Moreover, adequate efforts are required to explore and provide appropriate knowledge about the categorization of influential and non-influential design parameters with their suitable design spaces to guide researchers, drainage engineers, and stormwater management practitioners for effective and efficient planning, designing and optimization of GR at catchment-scales.This study employs a robust and comprehensive global sensitivity analysis (GSA) method known as the variogram analysis of response surfaces (VARS) for sensitivity analysis of GR design parameters. Firstly, a total of 13,999 sample points for 14 GR parameters of three layers (i.e., surface, soil and drainage mat) are generated by using the latin hypercube sampling technique and their factor spaces are decided based on design guidelines in current SWMM manuals. Following that, the PySWMM is used to simulate these design samples in a Monte-Carlo-type setting on a conceptual catchment of 0.01km2 (100m2 × 100m2) with 50% treatment area of GR, and the model responses (e.g., surface infiltration, surface outflow, storage volume, and peak flow) are estimated and applied for sensitivity analysis. Finally, VARS evaluates different sensitivity analysis metrics by using different model responses corresponding to their designed samples.Overall, the senstivity analysis results demonstrate that 8 out of 14 design parameters are highly influential on different model responses, however, the parameters’ sensitivity varies towards different model responses under different perturbation scales and rainfall conditions. Moreover, the selection of an effective range of design space of design parameters is necessary as it has a higher influence on model responses, while the parameters’ rankings and contributions to total sensitivity indices change with the range of design spaces. Furthermore, this research also provides an opportunity through VARS directional variogram index (an integrated sensitivity index) to study and understand the underlying mechanisms of design parameters under different perturbation scales with no extra computational burden. Senstivity analysis results will be presented with insights and recommendations for other regions, which will be helpful for decision-makers for effective planning, designing and implementation of GR. The findings of this parametric study would be helpful for the calibration and optimization of design parameters of GR for different case studies. 

The mechanical behavior of discontinuities is significantly affected by the characteristics of the infill present along them. However, fewer studies have been performed to assess the response to discontinuities influenced by unsaturated infill. This study performs a parametric numerical study in Fast Lagrangian Analysis of Continua (FLAC-2D) to understand the shearing behavior of discontinuities influenced by unsaturated infills. The study was conducted in two steps. The initial step involves a detailed parametric study to analyze the impact of infill and discontinuity characteristics on the observed shear behavior. The study was performed by varying the thickness-to-asperity ratio (t/a) from 0.5 to 3.0, the Joint Roughness Coefficient (JRC) from 2.4 to 18.7, the degree of infill saturation (Sr) from 0.7 to 1.0, and the normal stress (σ) from 0.1 to 1.5 MPa. In the second step, a shear strength criterion was postulated based on the numerical data generated in the parametric study. The functional form of the criterion was kept similar to the Mohr–Coulomb criterion for its easy implementation in numerical and analytical analyses. The criterion was comprehensive because it could consider the implications of the above-mentioned parameters for the shear response of discontinuities. It was seen that the shear strength of infilled rock joints is enhanced with increasing JRC and σ and decreasing t/a and Sr. The numerical model was capable of capturing the critical t/a ratio beyond which the shear strength becomes a constant value. The expected mechanisms are discussed for the parametric results. The developed strength criterion was concluded to be comprehensive and accurate for shearing discontinuities under different conditions. The practical application of the developed strength criterion is also demonstrated for a rock slope undergoing failure, and comparative analyses were made with the results estimated via existing popular criteria.

본 논문에서는 터널-지반 시스템의 거동을 합리적으로 해석하고 재료의 특성과 터널설계정수 평가를 위한 역해석 프로그램을 개발하였다. 이 프로그램은 유한차분법과 직접법을 조합한 역해석 기법을 이용하기 위하여 상용 프로그램인 FLAC(Fast Lagrangian Analysis of Continua)과 최적화 알고리즘을 이용하여 지하구조물의 역해석이 가능하도록 구성되었다. 역해석 알고리즘으로는 최적화 기법 중 미분계수를 구하지 않고 직접탐색이 가능한 로젠브록법(Rosenbrock Method)을 이용하였다. 이 연구를 통하여 개발된 역해석 알고리즘의 현장 적용성 검증을 위하여 4개 구간의 실제현장을 대상으로 현장 계측결과를 이용하여 역해석을 수행하였다. 역해석 과정에서 현장계측 변위에 대한 해석 대상지반의 최적함수를 파악하기 위하여 비선형 회귀분석(nonlinear regression analysis)을 실시하였다. 회귀분석은 지수함수와 분수함수를 이용하였으며, 이를 통하여 결정된 최적함수를 이용하여 계산된 총 변위를 역해석 입력 자료로 활용하였다. 이 연구결과로써 대상구조체의 실측변위를 이용한 역해석을 수행한 결과는 계측변위와 평균 4.5%의 오차율을 보였다. 따라서 이 연구에서 제안하는 역해석 기법이 터널 해석에 유용하게 적용될 수 있음을 알 수 있었다. In this paper, a back analysis program for analyzing the behavior of tunnel-ground system and evaluating the material properties and tunnel design parameters was developed. This program was designed to be able to implement the back analysis of underground structure by combination of using FLAC and optimized algorithm as direct method. In particular, Rosenbrock method which is able to do direct search without obtaining differential coefficient was adopted for the back analysis algorithm among optimization methods. This back analysis program was applied to the site to evaluate the design parameters. The back analysis was carried out using field measurement results from 5 sites. In the course of back analysis, nonlinear regression analysis was carried out to identify the optimum function of the measured ground displacement. Exponential function and fractional function were used for the regression analysis and total displacement calculated by optimum function was used as the back analysis input data. As a result, displacement recalculated through the back analysis using measured displacement of the structure showed 4.5% of error factor comparing to the measured data. Hence, the program developed in this study proved to be effectively applicable to tunnel analysis.

Variance-based sensitivity analysis is a well established tool for evaluating the contribution of the uncertainties in the inputs to the uncertainty in the output of a general mathematical model. While the literature on this subject is quite extensive, it has not found widespread use in metrological applications. In this article we present a succinct review of the fundamentals of sensitivity analysis, in a form that should be useful to most people familiarized with the Guide to the Expression of Uncertainty in Measurement (GUM). Through two examples, it is shown that in linear measurement models, no new knowledge is gained by using sensitivity analysis that is not already available after the terms in the so-called ‘law of propagation of uncertainties’ have been computed. However, if the model behaves non-linearly in the neighbourhood of the best estimates of the input quantities—and if these quantities are assumed to be statistically independent—sensitivity analysis is definitely advantageous for gaining insight into how they can be ranked according to their importance in establishing the uncertainty of the measurand.

Global sensitivity analysis (GSA) measures the variation of a model output as a function of the variations of the model inputs given their ranges. In this paper we consider variance-based GSA methods that do not rely on certain assumptions about the model structure such as linearity or monotonicity. These variance-based methods decompose the output variance into terms of increasing dimensionality called 'sensitivity indices', first introduced by Sobol' [25]. Sobol' developed a method of estimating these sensitivity indices using Monte Carlo simulations. McKay [13] proposed an efficient method using replicated Latin hypercube sampling to compute the 'correlation ratios' or 'main effects', which have been shown to be equivalent to Sobol's first-order sensitivity indices. Practical issues with using these variance estimators are how to choose adequate sample sizes and how to assess the accuracy of the results. This paper proposes a modified McKay main effect method featuring an adaptive procedure for accuracy assessment and improvement. We also extend our adaptive technique to the computation of second-order sensitivity indices. Details of the proposed adaptive procedure as wells as numerical results are included in this paper.

Ren, J.; Chen, B.; Li, Y.; Dai, J., and Men, L., 2020. Dynamic variation characteristics of the riparian zone temperature distribution under fluctuating water levels: Field experiments and numerical modeling. Journal of Coastal Research, 36(6), 1178–1196. Coconut Creek (Florida), ISSN 0749-0208.Understanding the variations in water and heat transfer along the riparian zone under water-level fluctuations is essential for river water management, groundwater extraction, and ecosystem sustainability. The main purpose of this study is to describe the dynamics of the temperature field of the Dongting Lake beach under the fluctuation in the water level and to quantify its main influencing factors. Taking the section of Dongting Lake beach as the research object, an in situ monitoring device was used to monitor the water level, water temperature, and temperature at different depths of the beach in real time for 55 days, and the hydrothermal coupling model of the Dongting Lake beach was calibrated and verified. The main factors affecting the temperature field of the beach were determined by the global sensitivity analysis method. The results show that the fluctuation in the continental beach temperature field is small in the horizontal direction, the stratification phenomenon is obvious in the vertical direction, the temperature gradually rises with increasing depth, and the daily changes are weakened. During the high water level, the deep temperature of the beach has no obvious gradient change in the vertical direction, and as the water level of the river decreases, the external environmental temperature has a greater influence on the internal temperature field of the beach, resulting in a relatively pronounced gradient change in the deep temperature at the low water level. The results of the Morris one at a time global sensitivity analysis show that the permeability coefficient (Ks) has the greatest influence on the sensitivity of the model, followed by the porosity (n) and soil thermal conductivity (λs). The saturated moisture content (θs), residual moisture content (θr), and soil-specific heat capacity (Cs) have no significant effect on the model.

Physiologically based pharmacokinetic (PBPK) models describe the absorption, distribution, metabolism, and excretion of chemicals. Probabilistic PBPK models can be used to produce distributional estimates of human equivalent doses (HEDs), which are external measures of human exposure predicted to result in a target internal dose, generated with Monte Carlo sampling and reverse dosimetry calculations. Very low HED percentiles represent individuals that are more sensitive to possible adverse effects of chemical exposures and are therefore frequently used in risk evaluation. Details of the parameter distributions used in probabilistic PBPK models impact HED distributions, but obtaining precise distributional estimates for all the parameters would be challenging. Therefore, we sought to determine methods that can identify the extent of model parameter influence on extreme HED percentiles. We first analyzed published PBPK models for dichloromethane and chloroform (for inhalation and oral exposures given 3 internal target levels each) by identifying the overall relative importance of parameters using global sensitivity analysis (GSA) methods. Then, we used a novel yet computationally expensive method to analyze the stability and sensitivity of extreme HED percentiles to input parameter distributions. Applying the traditional GSA methods allowed us to identify subsets of parameters most influential for accurately determining 1st and 99th percentiles, but the specific parameters included in those subsets varied for different models and exposure scenarios. Our results demonstrate that better characterizing PBPK model uncertainty by using precise distributional details for influential parameters informed by GSA methods may improve confidence in estimates of extreme percentiles of HEDs.