Variance-based Global Sensitivity Analysis Research Articles

Stochastic dynamics and sensitivity analysis of a multistage marine shafting system with uncertainties

The presence of uncertainties is ineluctable in marine shafting systems due to installation errors and varying operation conditions, where failure in quantifying these effects may cause excessive vibrations and even reliability problems of such systems. This paper concerns with the fast uncertainty quantification and sensitivity analysis of the stochastic dynamics for the marine shafting systems suffered propeller excitation and parameter uncertainties in bearing stiffnesses. A statistical surrogate model issued from the associating of a transfer matrix model for describing the shafting system together with a sparse generalized polynomial chaos expansion (gPCE) formalism for propagating probabilistic uncertainties is developed for the first time. A variance-based global sensitivity analysis is performed by evaluating Sobol indices from gPCE to quantitatively distinguish the relative importance of individual uncertain parameters and their interactions on the random vibration responses. The effects of uncertainties on the stochastic dynamic properties of the shafting system are subsequently investigated through the analysis of the uncertainty envelopes and probability density functions (PDFs) of the frequency responses, along with the associated sensitivity indices. Numerical results are compared with those obtained from the MCS with a large number of realizations, demonstrating the accuracy and significant computational advantage of the proposed methodology.

A Bayesian machine learning approach for inverse prediction of high-performance concrete ingredients with targeted performance

High-performance concrete (HPC) plays an important role in improving the sustainability and reliability of buildings and infrastructures. Machine learning predictive models have been used for predicting concrete performance from ingredients, however it remains a challenge to achieve inverse prediction of ingredients from targeted performances. This study proposes an in-house coded informatics-based materials analysis framework to enable computational design of HPC with targeted strength performance. The Gaussian processes (GP) emulator is used to construct the surrogate predictive model based-on 453 experimental measurements. The validity of the GP emulator is assessed using the leave-one-out cross-validation (LOO-CV) and also a separate validation dataset. The variance-based global sensitivity analysis, Sobol indices, is applied to understand the impact of physical ingredients on the HPC performances. The results suggest that the trained GP emulator can provide sufficiently accurate and reliable predictions, as well as reflect the real-world physicochemical nature of HPC materials. The inverse material design is achieved by the Bayesian inference method with a Markov chain Monte Carlo stochastic sampling method, the Metropolis-Hastings (MH) algorithm. Combining with the Bayesian inference method, the proposed design framework can infer a list of potential HPC formulae of a targeted performance, each evaluated by the likelihood of resulting in the targeted strength. The data-driven material analysis and design framework proposed in this study provides a novel approach to achieve performance-based design of HPC, with the potential to maximise resource efficiency and reduce economical cost. The methodology presented in this study can also be extended to be applied to a wide range of construction materials, targeting difference service performances including durability.

Computing a Global Degree of Rate Control for Catalytic Systems

In this paper, we discuss the concept and properties of variance-based global sensitivity analysis, as an expansion of local sensitivity metrics (such as the degree of rate control), for modeling a...

Input modeling and uncertainty quantification for improving volatile residential load forecasting

Residential load forecasting has been playing an increasingly important role in operation and planning of power systems. Over the recent years, accurate forecasts of individual loads have become ever more challenging due to the proliferation of distributed energy resources. This paper identifies and verifies the opportunity of improving load forecasting performance by incorporating suitable input modeling and uncertainty quantification, and proposes a two-stage approach that enjoys the following features. (1) It provides input modeling and quantifies the impact of input errors, rather than neglect or mitigate the impact—a prevalent practice of existing methods. (2) It propagates the impact of input errors into the ultimate point and interval predictions for the target customer’s load for improved predictive performance. (3) A variance-based global sensitivity analysis method is further proposed for input-space dimensionality reduction in both stages to enhance the computational efficiency. Numerical experiments show that the proposed two-stage approach outperforms competing load forecasting methods with respect to both point predictive accuracy and coverage ability of the predictive intervals achieved.

Global sensitivity analysis of low-velocity impact response of bio-inspired helicoidal laminates

The preform architectures and the variability of the constituents of carbon fiber reinforced polymer (CFRP) composites materials can affect their mechanical behaviors significantly. This paper describes a systematic analysis of the low-velocity impact response and energy absorption capacity of biomimetic architected CFRP laminates. High-fidelity multiscale Finite Element (FE) models considering constituent material property uncertainties are developed to evaluate the effect of pitch angles on the impact performance of Bouligand architected composite laminates. Experimental results extracted from open literature have been used to validate the low velocity impact response of the CFRPs predicted by the numerical model. Constituent material property uncertainties are identified as parametric variables, and the peak impact load and energy absorption responses of the bio-inspired CFRPs are obtained with the verified numerical models. The main effect sensitivity indices of the parameters are then calculated based on a variance-based global sensitivity analysis model. The presented studies clearly shows that smaller pitch angles and larger fiber longitudinal elastic modulus achieve more desirable impact resistance and better energy-absorption characteristics. This study aim to open up new possibilities for improving low velocity impact performance of CFRP composite laminates by adopting bionic design approach and considering constituent materials effect.

Key Physicochemical Properties Dictating Gastrointestinal Bioaccessibility of Microplastics-Associated Organic Xenobiotics: Insights from a Deep Learning Approach.

A potential risk from human uptake of microplastics is the release of plastics-associated xenobiotics, but the key physicochemical properties of microplastics controlling this process are elusive. Here, we show that the gastrointestinal bioaccessibility, assessed using an in vitro digestive model, of two model xenobiotics (pyrene, at 391-624 mg/kg, and 4-nonylphenol, at 3054-8117 mg/kg) bound to 18 microplastics (including pristine polystyrene, polyvinyl chloride, polyethylene terephthalate, polypropylene, thermoplastic polyurethane, and polyethylene, and two artificially aged samples of each polymer) covered wide ranges: 16.1-77.4% and 26.4-83.8%, respectively. Sorption/desorption experiments conducted in simulated gastric fluid indicated that structural rigidity of polymers was an important factor controlling bioaccessibility of the nonpolar, nonionic pyrene, likely by inducing physical entrapment of pyrene in porous domains, whereas polarity of microplastics controlled bioaccessibility of 4-nonylphenol, by regulating polar interactions. The changes of bioaccessibility induced by microplastics aging corroborated the important roles of polymeric structures and surface polarity in dictating sorption affinity and degree of desorption hysteresis, and consequently, gastrointestinal bioaccessibility. Variance-based global sensitivity analysis using a deep learning neural network approach further revealed that micropore volume was the most important microplastics property controlling bioaccessibility of pyrene, whereas the O/C ratio played a key role in dictating the bioaccessibility of 4-nonylphenol in the gastric tract.

Parameter Sensitivity and Uncertainty of Radiation Interception Models for Intercropping System

Abstract Estimating the interception of radiation is the first and crucial step for the prediction of production for intercropping systems. Determining the relative importance of radiation interception models to the specific outputs could assist in developing suitable model structures, which fit to the theory of light interception and promote model improvements. Assuming an intercropping system with a taller and a shorter crop, a variance-based global sensitivity analysis (EFAST) was applied to three radiation interception models (M1, M2 and M3). The sensitivity indices including main (Si) and total effects (STi) of the fraction of intercepted radiation by the taller (ftaller), the shorter (fshorter) and both intercrops together (fall) were quantified with different perturbations of the geometric arrangement of the crops (10-60 %). We found both ftaller and fshorter in M1 are most sensitive to the leaf area index of the taller crop (LAItaller). In M2, based on the main effects, the leaf area index of the shorter crop (LAIshorter) replaces LAItaller and becomes the most sensitive parameter for fshorter when the perturbations of widths of taller and shorter crops (Wtaller and Wshorter) become 40 % and larger. Furthermore, in M3, ftaller is most sensitive to LAItaller while fshorter is most sensitive to LAIshorter before the perturbations of geometry parameters becoming larger than 50 %. Meanwhile, LAItaller, LAIshorter, and Ktaller are the three most sensitive parameters for fall in all three models. From the results we conclude that M3 is the most plausible radiation interception model among the three models.

Dynamic reliability and variance-based global sensitivity analysis of pipes conveying fluid with both random and convex variables

Purpose This paper aims to solve the problem that pipes conveying fluid are faced with severe reliability failures under the complicated working environment. Design/methodology/approach This paper proposes a dynamic reliability and variance-based global sensitivity analysis (GSA) strategy with non-probabilistic convex model for pipes conveying fluid based on the first passage principle failure mechanism. To illustrate the influence of input uncertainty on output uncertainty of non-probability, the main index and the total index of variance-based GSA analysis are used. Furthermore, considering the efficiency of traditional simulation method, an active learning Kriging surrogate model is introduced to estimate the dynamic reliability and GSA indices of the structure system under random vibration. Findings The variance-based GSA analysis can measure the effect of input variables of convex model on the dynamic reliability, which provides useful reference and guidance for the design and optimization of pipes conveying fluid. For designers, the rankings and values of main and total indices have essential guiding role in engineering practice. Originality/value The effectiveness of the proposed method to calculate the dynamic reliability and sensitivity of pipes conveying fluid while ensuring the calculation accuracy and efficiency in the meantime.

Uncertainty quantification and global sensitivity analysis of double-diffusive natural convection in a porous enclosure

In this paper, detailed uncertainty propagation analysis (UPA) and variance-based global sensitivity analysis (GSA) are performed on the widely adopted double-diffuse convection (DDC) benchmark problem of a square porous cavity with horizontal temperature and concentration gradients. The objective is to understand the impact of uncertainties related to model parameters on metrics characterizing flow, heat and mass transfer processes, and to derive spatial maps of uncertainty and sensitivity indices which can provide physical insights and a better understanding of DDC processes in porous media. DDC simulations are computationally expensive and UPA and GSA require large number of simulations, so an appropriate strategy is developed to reduce the computational burden. The approach is built on two pillars: (a) an efficient numerical simulator based on the Fourier series method that generates training data, and (b) polynomial chaos expansion (PCE) meta-models that are trained using the simulator data, and then replace the numerical model in UPA and GSA. Assuming that the Rayleigh number (Ra), the solutal to thermal buoyancy ratio (Nb) and the Lewis number (Le) are the uncertain input variables, the results of UPA show that the zones of high temperature and concentration variability are located in the regions where the flow is mainly driven by the buoyancy effects. GSA indicates that Nb is the most influential parameter affecting the temperature and concentration fields, followed respectively by Ra and Le. For the heat-driven flow case (Nb>−1), the concentration field is more influenced by Le than Ra. For deeper understanding of uncertainty propagation, we estimate the bias introduced by replacing uncertain parameters by deterministic values. The resulting spatial maps of the difference between deterministic output and stochastic mean show that a deterministic approach leads to different zones where the temperature, concentration and velocity fields can be either overestimated or underestimated. The conclusions drawn in this work are likely to be helpful in different applications involving DDC in porous enclosures leading to convective circulation cells.

Uncertainties in projections of sandy beach erosion due to sea level rise: an analysis at the European scale

Sea level rise (SLR) will cause shoreline retreat of sandy coasts in the absence of sand supply mechanisms. These coasts have high touristic and ecological value and provide protection of valuable infrastructures and buildings to storm impacts. So far, large-scale assessments of shoreline retreat use specific datasets or assumptions for the geophysical representation of the coastal system, without any quantification of the effect that these choices might have on the assessment. Here we quantify SLR driven potential shoreline retreat and consequent coastal land loss in Europe during the twenty-first century using different combinations of geophysical datasets for (a) the location and spatial extent of sandy beaches and (b) their nearshore slopes. Using data-based spatially-varying nearshore slope data, a European averaged SLR driven median shoreline retreat of 97 m (54 m) is projected under RCP 8.5 (4.5) by year 2100, relative to the baseline year 2010. This retreat would translate to 2,500 km2 (1,400 km2) of coastal land loss (in the absence of ambient shoreline changes). A variance-based global sensitivity analysis indicates that the uncertainty associated with the choice of geophysical datasets can contribute up to 45% (26%) of the variance in coastal land loss projections for Europe by 2050 (2100). This contribution can be as high as that associated with future mitigation scenarios and SLR projections.

Online monitoring and control of a cyber-physical manufacturing process under uncertainty.

Recent technological advancements in computing, sensing and communication have led to the development of cyber-physical manufacturing processes, where a computing subsystem monitors the manufacturing process performance in real-time by analyzing sensor data and implements the necessary control to improve the product quality. This paper develops a predictive control framework where control actions are implemented after predicting the state of the manufacturing process or product quality at a future time using process models. In a cyber-physical manufacturing process, the product quality predictions may be affected by uncertainty sources from the computing subsystem (resource and communication uncertainty), manufacturing process (input uncertainty, process variability and modeling errors), and sensors (measurement uncertainty). In addition, due to the continuous interactions between the computing subsystem and the manufacturing process, these uncertainty sources may aggregate and compound over time. In some cases, some process parameters needed for model predictions may not be precisely known and may need to be derived from real time sensor data. This paper develops a dynamic Bayesian network approach, which enables the aggregation of multiple uncertainty sources, parameter estimation and robust prediction for online control. As the number of process parameters increase, their estimation using sensor data in real-time can be computationally expensive. To facilitate real-time analysis, variance-based global sensitivity analysis is used for dimension reduction. The proposed methodology of online monitoring and control under uncertainty, and dimension reduction, are illustrated for a cyber-physical turning process.

Global sensitivity analysis of the ADAM dispersion module: Jack Rabbit II test case

Abstract This paper provides the result of a parametric sensitivity study conducted on the atmospheric dispersion module of the Accident Damage Analysis Module for consequence assessment, developed by the European Commission to support the EU competent authorities for the implementation of the Seveso Directive in their countries or other legislation associated with chemical safety and security. A variance-based Global Sensitivity Analysis was conducted on a series of reference scenarios build by using the trials of the Jack Rabbit II coordinated model inter-comparison exercise, in order to establish the impact of input parameters on the model output uncertainty.

Global Sensitivity Analysis of the Static Performance of Concrete Gravity Dam from the Viewpoint of Structural Health Monitoring

Structural Health Monitoring (SHM) is becoming the fourth driving force of engineering science and technology progress, in addition to the basic theory, numerical simulation and model test. In this paper, a definition of dam SHM is presented, its basic connotation is analyzed, and the general problems in existing researches are summarized. Then the sensitivity analysis of the static performance of concrete gravity dam is reviewed. For a hypothetical concrete gravity dam, a preliminary nonlinear finite element model is established. By means of the variance-based global sensitivity analysis method, phenomenological analysis of the static performance of the dam is carried out from three different horizons. And then the results are discussed in detail according to the common components of SHM. Overall, this paper provides a framework for sensitivity analysis of dams, or a way to explore the complexity of the dam system. In the long run, this paper should still be positioned as a generic and qualitative study in view of the complexity of dam system. There are still many issues as pointed out in the text need to be further understood and studied, and sensitivity analysis is a good tool.

Probabilistic-based structural assessment of a historic stone arch bridge

A probabilistic analysis approach for reliability-based assessment of masonry arch bridges is presented in this work. The methodology is tested on a medieval in-service construction located in Galicia, northwest of Spain. To estimate its ultimate load-carrying capacity, two different numerical approaches are employed; a three-dimensional non-linear finite element model and a two-dimensional rigid blocks limit analysis model. Aiming to alleviate the computational burden associated with the probabilistic analysis procedure, a surrogate modelling strategy is adopted. A complete understanding of the influence of model input parameters on the limit load of the structure is attained through the employment of global variance-based sensitivity analysis. The reliability assessment procedure is subsequently carried out, allowing to estimate the bridge failure probability. A difference of approximately 33% is obtained between the reliability index values drawn from both structural modelling strategies, so revealing the key role played by transversal effects on the strength capacity of masonry arch bridges. The proposed probabilistic assessment framework might be deemed as a useful tool, from which more reliable and objective information about the actual safety condition of existing masonry arch bridges can be derived, taking advantage of readily available numerical tools, but still demanding an affordable computational effort.

Bayesian identification of a projection-based reduced order model for computational fluid dynamics

In this paper we propose a Bayesian method as a numerical way to correct and stabilise projection-based reduced order models (ROM) in computational fluid dynamics problems. The approach is of hybrid type, and consists of the classical proper orthogonal decomposition driven Galerkin projection of the laminar part of the governing equations, and Bayesian identification of the correction term mimicking both the turbulence model and possible ROM-related instabilities given the full order data. In this manner the classical ROM approach is translated to the parameter identification problem on a set of nonlinear ordinary differential equations. Computationally the inverse problem is solved with the help of the Gauss-Markov-Kalman smoother in both ensemble and square-root polynomial chaos expansion forms. To reduce the dimension of the posterior space, a novel global variance based sensitivity analysis is proposed.

Filamentous organisms degrade oxygen transfer efficiency by increasing mixed liquor apparent viscosity: Mechanistic understanding and experimental verification

Recent findings have demonstrated that activated sludge morphology significantly impacts oxygen transfer efficiency (OTE) in the activated sludge process. In this study, we developed a mechanistic understanding of this impact. Mixed liquor samples collected from a domestic wastewater treatment plant (WWTP) were blended with a bulking activated sludge from a bench scale reactor (BSR) cultured on synthetic wastewater to manipulate various morphological parameters such as the settled sludge volume (SV), the sludge volume index (SVI), and the specific filament length (SFL). The filaments that were present in the blended sludges consisted largely of Type 0041 and Type 021N, which are commonly found in WWTPs that treat domestic wastewater. Variations in sludge morphology, as quantified by settled sludge volume after 30 min (SV30), SVI, and SFL, systematically affected the mixed liquor apparent viscosity (μapp), which consequently impacted OTE. An increase in the SFL from 9.61 × 106 μm g−1 to 6.88 × 107 μm g−1 resulted in a 41.4% increase in apparent viscosity and a 24.6% decrease in volumetric mass transfer coefficient (KLa). A new parameter, named the ultimate settleability (SVULT), was developed by curve fitting the SV versus time data and found to relate with μapp through an expanded form of the Einstein Equation for the viscosity. Therefore, SVULT is a corollary for the particle volume fraction that incorporates effects of both the sludge morphology and mass concentration on μapp. Theoretical derivation revealed that an increase in SVULT resulted in an increase in μapp, which reduced oxygen transfer by increasing the air bubble size and reducing refreshment of the liquid at the gas-liquid interface. The KLa was found to be inversely proportional to μapp0.75 through fitting the experimental data with the theoretical model. Using a variance-based global sensitivity analysis, three operating parameters that have the most impact on oxygen transfer were identified: the power input per unit volume, the superficial gas flowrate, and the μapp.

An experimentally validated rubber shear spring model for vibrating flip-flow screens

Vibrating flip-flow screens (VFFS) provide an effective solution for screening highly moist and fine-grained minerals, and the dynamic response of the main and the floating screen frames largely accounts for a VFFS’s screening performance and its processing capacity. An accurate dynamic model of the rubber shear springs inserted between the frames of the VFFS is critical for its dynamic analysis but has rarely been studied in detail. In this paper, a variance-based global sensitivity analysis is applied to actually illustrate that the rubber shear spring is the most important component for the dynamics of VFFS. Then a nonlinear rubber shear spring model is proposed to predict its amplitude and frequency dependency, which is described by a friction model and a fractional derivative viscoelastic model, respectively, and the elasticity is predicted by a nonlinear spring. The reasonability of the proposed model is verified by experimental cyclic tests of the rubber shear spring. Comparisons between the newly proposed model and other classic models, including the Generalized Maxwell model, adopted for the dynamic analysis of the VFFS are carried out, and experimental tests of an industrial VFFS’s dynamic response show that dynamics of the VFFS can be better described using the proposed model than the existing models. Furthermore, the method of the global sensitivity analysis is also applied to the newly VFFS dynamic model to calculate the sensitivities of model outputs caused by the input parameters. The results reveal that the dynamic response of an operating VFFS is most sensitive to changes in the stiffness of the rubber shear spring, followed by the mass of the floating screen frames.

Surrogate-assisted global sensitivity analysis: an overview

Surrogate models are popular tool to approximate the functional relationship of expensive simulation models in multiple scientific and engineering disciplines. Successful use of surrogate models can provide significant savings of computational cost. However, with a variety of surrogate model approaches available in literature, it is a difficult task to select an appropriate one at hand. In this paper, we present an overview of surrogate model approaches with an emphasis of their application for variance-based global sensitivity analysis, including polynomial regression model, high-dimensional model representation, state-dependent parameter, polynomial chaos expansion, Kriging/Gaussian Process, support vector regression, radial basis function, and low rank tensor approximation. The accuracy and efficiency of these approaches are compared with several benchmark examples. The strengths and weaknesses of these surrogate models are discussed, and the recommendations are provided for different types of applications. For ease of implementations, the packages, as well as toolboxes, of surrogate model techniques and their applications for global sensitivity analysis are collected.

Sensitivity Analysis of the DART Model for Forest Mensuration with Airborne Laser Scanning

Airborne Laser Scanning (ALS) measurements are increasingly vital in forest management and national forest inventories. Despite the growing reliance on ALS data, comparatively little research has examined the sensitivity of ALS measurements to varying survey conditions over commercially important forests. This study investigated: (i) how accurately the Discrete Anisotropic Radiative Transfer (DART) model was able to replicate small-footprint ALS measurements collected over Irish conifer plantations, and (ii) how survey characteristics influenced the precision of discrete-return metrics. A variance-based global sensitivity analysis demonstrated that discrete-return height distributions were accurately and consistently simulated across 100 forest inventory plots with few perturbations induced by varying acquisition parameters or ground topography. In contrast, discrete return density, canopy cover and the proportion of multiple returns were sensitive to fluctuations in sensor altitude, scanning angle, pulse repetition frequency and pulse duration. Our findings corroborate previous studies indicating that discrete-return heights are robust to varying acquisition parameters and may be reliable predictors for the indirect retrieval of forest inventory measurements. However, canopy cover and density metrics are only comparable for ALS data collected under similar acquisition conditions, precluding their universal use across different ALS surveys. Our study demonstrates that DART is a robust model for simulating discrete-return measurements over structurally complex forests; however, the replication of foliage morphology, density and orientation are important considerations for radiative transfer simulations using synthetic trees with explicitly defined crown architectures.

Uncertain Frequency Responses of Clamp-Pipeline Systems Using an Interval-Based Method

Due to manufacturing errors and material deteriorations in the metal rubber of clamps, the clamp stiffness of the pipeline is uncertain. This paper presents a non-intrusive multi-dimensional Chebyshev polynomial approximation method (M-CPAM) to evaluate uncertain characteristics of the frequency response function (FRF) of the clamp-pipeline system (CPS), where the clamp stiffness parameters are taken as unknown but bounded interval variables. Firstly, a finite element model of the clamp-pipeline system is established. Secondly, the variance-based global sensitivity analysis is implemented to determine significant stiffness parameters. Then, the uncertain intervals of the clamp stiffness are measured by experiments and the dispersion of the clamp stiffness is described. Finally, based on the measured stiffness interval, the uncertain frequency responses of the CPS under different tightening torques are analyzed by the proposed M-CPAM, and the effectiveness of simulation results is verified by experiments. Compared with the results obtained from the Monte Carlo simulation, the experimental measurements, and the polynomial chaos expansion, the proposed M-CPAM provides a more accurate, time-saving and practical method for solving the uncertain frequency responses of the CPS with interval stiffness variables. The results show that the clamp stiffness has great dispersion under the same tightening torque. A frequency shift phenomenon will be observed when the clamp stiffness is uncertain. Moreover, the dispersion of the frequency response of the CPS tends to be concentrated with the increase of the tightening torques.