Variance-based Sensitivity Analysis Research Articles

Torsional Vibration and Sensitivity Analysis of Microcantilever in Liquid

Development of microsystems and ever-increasing advances of nanotechnology have resulted in growing applications of microcantilevers (MCs), including Atomic Force Microscopy (AFM). In AFM, transverse vibration of microfiber from a liquid medium results in resonance of unwanted hydrodynamic and electrostatic forces, which can be minimized by torsional mode. In the present study, the differential equation of the vibrational motion is extracted by acquiring the hydrodynamic force applied to MCs aiming to investigate the torsional vibration behavior of MCs in a liquid medium; and the extracted equation is solved to study the behavior of MCs in a liquid medium. Considering the significant effect of MC geometry on its torsional vibrations in a liquid medium, Sobol's variance-based sensitivity analysis method was utilized to investigate the effectiveness of MC geometry on torsional vibration. The sensitivity analysis results show that length and width have the most significant effects on the quality factor and the resonance frequency of MCs.

Machine learning method for shale gas adsorption capacity prediction and key influencing factors evaluation

Shale gas plays a pivotal role in the global energy landscape, emphasizing the need for accurate shale gas-in-place (GIP) prediction to facilitate effective production planning. Adsorbed gas in shale, the primary form of gas storage under reservoir conditions, is a critical aspect of this prediction. In this study, a machine learning Gaussian process regression (GPR) model for methane adsorption prediction was established and validated using published experimental data. Five typical variables, i.e., total organic carbon (TOC), clay minerals, temperature, pressure, and moisture were considered, which were derived from the Marine shale of the Longmaxi formation in the Sichuan Basin through correlation analysis. The performance of the GPR model was compared with the widely used an extreme gradient boosting model. It turned out that our GPR model had better accuracy for predicting methane adsorption in shale with an average relative error of less than 3%. Furthermore, a variance-based sensitivity analysis method in conjunction with kernel density estimation theory was employed to conduct a global sensitivity analysis, quantifying the nonlinear influence of each variable methane adsorption. The findings indicate that TOC is the most significant factor affecting methane adsorption, while clay minerals have a limited direct impact but can enhance their influence through interactions with other influencing factors. Finally, based on the GPR model, a GIP prediction method was proposed that eliminates the need for calculating the density of the adsorbed phase. These findings are expected to extend the shale gas reserve assessment methodologies and offer valuable insight for further exploring the adsorption mechanisms of shale gas.

Stochastic critical buckling speed analysis of rim-driven rotating composite plate using NURBS-based isogeometric approach and HSDT

This article is the first attempt in the open literature to investigate the impact of uncertainty in material properties on the critical buckling speed of rim-driven rotating laminated plates. The formulations are constructed using the isogeometric approach (IGA) and higher-order shear deformation theory (HSDT). Coriolis and centrifugal forces resulting from rotation are taken into consideration. The results of the current formulation are compared to the previous results and validated. The accuracy and flexibility of the RBFN-based surrogate model, designed for uncertainty analysis, is verified by comparing the result with Monte Carlo simulation (MCS). Through a variety of parametric experiments, the critical buckling speed of rotating laminates driven by a rim is stochastically analyzed. Variance-based sensitivity analysis is employed to identify the influence of individual material properties on the critical buckling speed. Further, the impact of sensitive properties on the probability of structural failure is estimated. This research can be used to forecast the probability of failure of a structure at various levels of material uncertainty associated with it.

Efficient sensitivity analysis for biomechanical models with correlated inputs.

In most variance-based sensitivity analysis (SA) approaches applied to biomechanical models, statistical independence of the model input is assumed. However, often the model inputs are correlated. This might alter the interpretation of the SA results, which may severely impact the guidance provided during model development and personalization. Potential reasons for the infrequent usage of SA techniques that account for input correlation are the associated high computational costs, especially for models with many parameters, and the fact that the input correlation structure is often unknown. The aim of this study was to propose an efficient correlated global sensitivity analysis method by applying a surrogate model-based approach. Furthermore, this article demonstrates how correlated SA should be interpreted and how the applied method can guide the modeler during model development and personalization, even when the correlation structure is not entirely known beforehand. The proposed methodology was applied to a typical example of a pulse wave propagation model and resulted in accurate SA results that could be obtained at a theoretically 27,000× lower computational cost compared to the correlated SA approach without employing a surrogate model. Furthermore, our results demonstrate that input correlations can significantly affect SA results, which emphasizes the need to thoroughly investigate the effect of input correlations during model development. We conclude that our proposed surrogate-based SA approach allows modelers to efficiently perform correlated SA to complex biomechanical models and allows modelers to focus on input prioritization, input fixing and model reduction, or assessing the dependency structure between parameters.

Assessing Climate Sensitivity and Mechanisms in a One-Dimensional Climate Energy Balance Model

Addressing the pressing concerns surrounding climate sensitivity, particularly within the context of Earth's changing climate, remains a pivotal endeavor. In this paper, the earth global temperature variation modeled by a one-dimensional climate energy balance model (EBM) is studied using a variance-based sensitivity analysis. The outcomes of this study offer a comprehensive analysis on each parameter that govern Earth's climate dynamics. Specifically, the analyses highlight that land albedo possesses the most substantial First-Order Sobol indices; the solar multiplier and the constant coefficient in the linearized Stefan-Boltzmann Law emerge as the second and third-largest contributor to Sobol indices, while the sensitivity of albedo of ice, temperature dependent coefficient of linearized Stefan-Boltzmann Law, and Transfer Coefficient remain insignificance. The analysis also suggests the non-negligible role of ice-albedo feedback and supports the hypothesis of the "Snowball Earth". This research holds significance as it uniquely addresses Earth's climate sensitivity using a one-dimensional Energy Balance Model, offering fundamental yet essential insights into the dynamics of earth's climate system, particularly its temperature variations.

What really matters to reduce the energy demand of household electronics? Global sensitivity analysis of circular economy strategies for the United Kingdom

Limiting the global temperatures to +1.5 °C from pre-industrial levels requires achieving net-zero greenhouse gas emissions by 2050. This should be achieved across all sectors, and for electrical and electronic equipment (EEE) the promotion of repair, lifetime extension and other Circular Economy (CE) strategies are often proposed as the main areas for intervention. However, few studies have quantified and compared the effectiveness of different CE strategies at reducing emissions at a national level and into the future. To fill this gap, an extended dynamic stock model was combined with a device energy consumption model to anticipate the embodied, operational, and repair energy requirements arising from the stocks and flows of seven devices up to 2050 in the United Kingdom (UK). To understand the relative influence of all model inputs on device energy demand in 2050, a variance-based sensitivity analysis was performed using the Sobol method. The results show that device size is the most significant variable for six out of the seven devices. Whereas substantial increases in device lifetime and repair rates were shown not to be significant in reducing energy demand. A reduction of 30% of energy demand by 2050 is possible for almost all EEE devices, except laptops and TVs. However, delivering these savings requires significant changes to consumption behaviours such as decreasing device size by about 40% or decreasing ownership rates by approximately two thirds through shared ownership. This analysis prioritises the most impactful strategies to reduce the total energy demand of EEE in the UK.

An Uncertainty Model for Strain Gages Using Monte Carlo Methodology.

For the purpose of validation and identification of mechanical systems, measurements are indispensable. However, they require knowledge of the inherent uncertainty to provide valid information. This paper describes a method on how to evaluate uncertainties in strain measurement using electric strain gages for practical engineering applications. Therefore, a basic model of the measurement is deduced that comprises the main influence factors and their uncertainties. This is performed using the example of a project dealing with strain measurement on the concrete surface of a large-span road bridge under static loading. Special attention is given to the statistical modeling of the inputs, the underlying physical relationship, and the incorporation and the impact of nonlinearities for different environmental conditions and strain levels. In this regard, also experiments were conducted to quantify the influence of misalignment of the gages. The methodological approach used is Monte Carlo simulation. A subsequent variance-based sensitivity analysis reveals the degree of nonlinearity in the relationship and the importance of the different factors to the resulting probability distribution. The developed scheme requires a minimum of expert knowledge of the analytical derivation of measurement uncertainties and can easily be modified for differing requirements and purposes.

Sensitivity analysis of fifth generation district heating and cooling coupled with borehole thermal energy storage with respect to cooling adoption

Fifth generation district heating and cooling (5GDHC) is a promising solution for decarbonising building thermal demands, as it allows for simultaneous heating and cooling through a bi-directional network. This paper aims to investigate the general performance of 5GDHC under uncertainty. Initially, an uncertainty analysis is performed on a 5GDHC model in a case study, revealing significant variation in economic, technical, and environmental performance due to uncertain parameters. Subsequently, variance-based global sensitivity analysis is used to rank the uncertain parameters based on their impact on the economic performance of 5GDHC. The results identify cooling adoption rate, borehole pricing, and discount rate as the most influential parameters. Lastly, factors mapping demonstrates that cooling adoption rate within 0.6-0.9, low borehole costs, low discount rates, and high gas prices will drive the switch to 5GDHC. Overall, this study emphasizes the general applicability of 5GDHC.

Estimating global identifiability using conditional mutual information in a Bayesian framework

A novel information-theoretic approach is proposed to assess the global practical identifiability of Bayesian statistical models. Based on the concept of conditional mutual information, an estimate of information gained for each model parameter is used to quantify the identifiability with practical considerations. No assumptions are made about the structure of the statistical model or the prior distribution while constructing the estimator. The estimator has the following notable advantages: first, no controlled experiment or data is required to conduct the practical identifiability analysis; second, unlike popular variance-based global sensitivity analysis methods, different forms of uncertainties, such as model-form, parameter, or measurement can be taken into account; third, the identifiability analysis is global, and therefore independent of a realization of the parameters. If an individual parameter has low identifiability, it can belong to an identifiable subset such that parameters within the subset have a functional relationship and thus have a combined effect on the statistical model. The practical identifiability framework is extended to highlight the dependencies between parameter pairs that emerge a posteriori to find identifiable parameter subsets. The applicability of the proposed approach is demonstrated using a linear Gaussian model and a non-linear methane-air reduced kinetics model. It is shown that by examining the information gained for each model parameter along with its dependencies with other parameters, a subset of parameters that can be estimated with high posterior certainty can be found.

Iterative hierarchical clustering algorithm for automated operational modal analysis

Recent developments in sensors and data processing made the structural health monitoring (SHM) sector expanding to big-data field, particularly when continuous long-term strategies are implemented. Nevertheless, main shortcomings are due to the identification and extraction of modal features. In fact, although machine learning methods have been implemented to automate modal identification processes, intense user interaction and time-consuming procedures are still required, limiting the extensive use of these techniques. In order to provide a fully automated procedure capable of identifying and extracting modal properties from covariance driven SSI analyses, an innovative and flexible algorithm for Iterative Hierarchical Clustering Analysis (IHCA) is proposed. To evaluate the stability and robustness of the IHCA method, a Variance-Based Global sensitivity Analysis (VBGA) was performed considering a numerical and experimental case study. The outcomes demonstrated that the IHCA is stable in clustering the physical structural modes and selecting the most representative modal features.

Developing an airport sustainability evaluation index through composite indicator approach

This paper proposes a holistic definition of airport sustainability comprising social, economic, operational, and environmental dimensions. Methodologically, a composite indicator approach is applied to build the Airport Sustainability Evaluation Index (ASEI), which aims to benchmark airports' sustainability performance across the four dimensions. To justify the issue of subjectivity in composite indicator building, two different methods are used in each of the normalization, weighting, and aggregation processes. Consequently, this forms eight composite indicator building schemes. Then, a variance-based sensitivity analysis, average shift in ranking (ASR), and Cronbach's alpha test are performed to examine the sensitivity and reliability among the eight schemes. Schiphol airport is selected as a demonstration to validate the ASEI with its data from 2012 to 2021 as inputs. The results reveal a significant consensus among the eight schemes in identifying the outstanding and bottom performers across the analyzed period. Additionally, weighting is found to be the most influential composite indicator building process. Further, the scheme with the most significant contribution to the result reliability found in this paper is re-scaling as the normalization method, Benefit-of-the-doubt (BoD) as the weighting method, and Non-compensatory multi-criteria approach (NCMC) as the aggregation method.

Effect of uncertainty of material parameters on stress triaxiality and Lode angle in finite elasto-plasticity—A variance-based global sensitivity analysis

This work establishes a computational framework for the quantification of the effect of uncertainty of material model parameters on extremal stress triaxiality and Lode angle values in plastically deformed devices, whereby stress triaxiality and Lode angle are accepted as key indicators for damage initiation in metal forming processes. Attention is paid to components, the material response of which can be represented as elasto-plastic with proportional hardening as a prototype model, whereby the finite element method is used as a simulation approach generally suitable for complex geometries and loading conditions. Uncertainty about material parameters is characterized resorting to probability theory. The effects of material parameter uncertainty on stress triaxiality and Lode angle are quantified by means of a variance-based global sensitivity analysis. Such sensitivity analysis is most useful for apportioning the variance of the stress triaxiality and Lode angle to the uncertainty on material properties. The practical implementation of this sensitivity analysis is carried out resorting to a Gaussian process regression, Bayesian probabilistic integration and active learning in order to decrease the associated numerical costs. An example illustrates the proposed framework, revealing that parameters governing plasticity affect stress triaxiality and Lode angle the most.

On quantifying uncertainty in lightning strike damage of composite laminates: A hybrid stochastic framework of coupled transient thermal-electrical simulations

Lightning strike damage can severely affect the thermo-mechanical performance of composite laminates. It is essential to quantify the effect of lightning strikes considering the inevitable influence of material and geometric uncertainties for ensuring the operational safety of aircraft. This paper presents an efficient support vector machine (SVM)-based surrogate approach coupled with computationally intensive transient thermal-electrical finite element simulations to quantify the uncertainty in lightning strike damage. The uncertainty in epoxy matrix thermal damage and electrical responses of unprotected carbon/epoxy composite laminates is probabilistically quantified considering the stochasticity in temperature-dependent multi-physical material properties and ply orientations. Further, the SVM models are exploited for variance-based global sensitivity analysis to investigate the input parameters' relative influence on the lightning strike-induced damage behavior. Due to the adoption of a coupled SVM-based simulation approach here, it has become possible to carry out a comprehensive uncertainty quantification leading to complete probabilistic descriptions of the electrical and lightning damage parameters despite the requirement of performing a large number of computationally intensive function evaluations. The results reveal that source-uncertainty of the unprotected laminates significantly influences the epoxy matrix decomposition, electrical current density and electric potential, wherein longitudinal electrical conductivity is most sensitive to stochastic variations followed by other electrical, thermal and geometric parameters.

The application of semantic modelling to map pollination service provisioning at large landscape scales

Mapping ecosystem services (ES), including crop pollination by wild insect pollinators, is challenging due to the number of variables involved and the spatial-temporal dimensions of their interactions. To enhance the synergistic relationship between pollination service and crop yield in agricultural landscapes, a better appreciation of the spatial dynamics of pollination service provisioning is needed. Spatially explicit modelling approaches have been used to investigate how different land cover types influence the distribution and abundance of wild bee pollinators in agricultural landscapes. However, an integrated dynamic and spatial modelling framework is needed to address the complexities of pollination supply mapping at the landscape scale. The Artificial Intelligence for Environment and Sustainability (ARIES) framework is a collaborative, spatially explicit and integrated tool for ES assessment. We applied a set of high-resolution process-based pollination models within ARIES to represent landscape capacity to supply pollination by wild bees at the local scale in the Canadian prairies. We also developed a systematic approach to perform a global sensitivity analysis by using a surrogate model (Gaussian Process Regression) and variance-based sensitivity analysis for the selected uncertain key parameters of the model. We modelled pollination dynamics through the mechanistic behavior of native bee guilds, including foraging distance, nesting ability, flight activity, the relative importance of bee guilds, and seasonal variation of floral resources. We focused on three guilds, bumblebees, sweat bees and mining bees, which differed by their nesting habits, floral preferences, and flight distances. We found that over 45% of pollination-dependent croplands in our study area lack wild pollination. The global sensitivity analysis revealed the significance of all key parameters, with seasonal activity across guilds identified as the key driving factors. Our results highlight the significance of the ecological role of wild bees in agricultural landscapes and the sensitivity analysis underscores the importance of temporal dynamics in ecological modeling and pollination.

Bayesian parameter identification in electrochemical model for lithium-ion batteries

Electrochemical models can characterize the internal behavior of cells and are powerful and effective tools for the design and management of batteries. This study proposes a comprehensive framework of Bayesian parameter identification to determine the parameter distributions in the electrochemical model and to estimate the global sensitivity of the parameters for lithium-ion batteries. Bayesian inference in parameter identification can simultaneously determine accurate parameter estimates and parameter identifiability, given specific voltage measurements. Among the several parameters in the pseudo-two-dimensional model, 15 parameters are selected to estimate the posterior distributions. The reconstructed voltage curves through the estimated parameter distributions are consistent with the reference voltages, with relative errors of less than 0.7% at various discharge rates. Changes in the parameter distributions and identifiability were investigated for different discharge rates through the estimated joint and marginal distributions of the parameters. Moreover, based on variance-based global sensitivity analysis, the identifiability of the electrochemical parameters according to the discharge rates is quantitatively analyzed. We demonstrate that the Bayesian parameter identification simultaneously obtains the parameter distributions and identifiability, considering the correlation between various parameters. The proposed framework can help to analyze the behaviors of batteries according to specific operating conditions and materials.

Fusing time-varying mosquito data and continuous mosquito population dynamics models

Climate change is arguably one of the most pressing issues affecting the world today and requires the fusion of disparate data streams to accurately model its impacts. Mosquito populations respond to temperature and precipitation in a nonlinear way, making predicting climate impacts on mosquito-borne diseases an ongoing challenge. Data-driven approaches for accurately modeling mosquito populations are needed for predicting mosquito-borne disease risk under climate change scenarios. Many current models for disease transmission are continuous and autonomous, while mosquito data is discrete and varies both within and between seasons. This study uses an optimization framework to fit a non-autonomous logistic model with periodic net growth rate and carrying capacity parameters for 15 years of daily mosquito time-series data from the Greater Toronto Area of Canada. The resulting parameters accurately capture the inter-annual and intra-seasonal variability of mosquito populations within a single geographic region, and a variance-based sensitivity analysis highlights the influence each parameter has on the peak magnitude and timing of the mosquito season. This method can easily extend to other geographic regions and be integrated into a larger disease transmission model. This method addresses the ongoing challenges of data and model fusion by serving as a link between discrete time-series data and continuous differential equations for mosquito-borne epidemiology models.

Variance-based sensitivity analysis of oil spill predictions in the Red Sea region

To support accidental spill rapid response efforts, oil spill simulations may generally need to account for uncertainties concerning the nature and properties of the spill, which compound those inherent in model parameterizations. A full detailed account of these sources of uncertainty would however require prohibitive resources needed to sample a large dimensional space. In this work, a variance-based sensitivity analysis is conducted to explore the possibility of restricting a priori the set of uncertain parameters, at least in the context of realistic simulations of oil spills in the Red Sea region spanning a two-week period following the oil release. The evolution of the spill is described using the simulation capabilities of Modelo Hidrodinâmico, driven by high-resolution metocean fields of the Red Sea (RS) was adopted to simulate accidental oil spills in the RS. Eight spill scenarios are considered in the analysis, which are carefully selected to account for the diversity of metocean conditions in the region. Polynomial chaos expansions are employed to propagate parametric uncertainties and efficiently estimate variance-based sensitivities. Attention is focused on integral quantities characterizing the transport, deformation, evaporation and dispersion of the spill. The analysis indicates that variability in these quantities may be suitably captured by restricting the set of uncertain inputs parameters, namely the wind coefficient, interfacial tension, API gravity, and viscosity. Thus, forecast variability and confidence intervals may be reasonably estimated in the corresponding four-dimensional input space.

Potential and Benefit of Green Roof Energy Renovation of Existing Residential Buildings with a Flat Roof in Belgrade

Green roofs are considered to be one of the optimal tools for saving energy and protecting the environment in developed countries. In this paper, an analysis of the possible application of green roofs on existing residential buildings with flat roofs is presented. In the economic analysis, models of existing buildings in Belgrade, with two different types of green roofs, are studied. A key indicator of investment profitability in this investigation is the net present value (NPV) of the green roof project. Besides the private economic impact, other aspects of green roof applications, significant for sustainable development, have been highlighted. The values of the reductions in the annual energy needed for heating and cooling are compared for different scenarios. A maximum energy saving of 22% in the heating season is determined in the building energy simulation program for the model with an intensive green roof. Life cycle profit analysis was based on the probabilistic approach. The corresponding variance-based sensitivity analysis determined the impact of various parameters on the final result. In all models, the first order sensitivity index, which measures the impact of the number of residential units on the NPV, ranges from 12.2% to 63.6%. Sensitivity analysis showed that the benefit of property value increase has the highest influence on the calculated NPV in scenarios that account for this benefit. The obtained results in those scenarios indicate that the most probable NPV at the end of the life cycle is EUR 43/m2 and EUR 82/m2 for extensive and intensive green roofs, respectively.

Bayesian Model Updating for Structural Dynamic Applications Combing Differential Evolution Adaptive Metropolis and Kriging Model

The Bayesian model updating approach has attracted much attention by providing the most probable values (MPVs) of physical parameters and their uncertainties. However, the Bayesian approach has challenges in high-dimensional problems and requires high computational costs in large-scale engineering structures dealing with structural dynamics. This study proposes a new Bayesian updating framework using the Differential Evolution Adaptive Metropolis (DREAM) algorithm to enhance the Bayesian approach’s performance and computational efficiency. In addition, two time-saving strategies are proposed. Firstly, variance-based global sensitivity analysis is used to eliminate insignificant parameters to model responses and reduce model dimensionality. Secondly, a fast-running kriging model is employed as a surrogate of the time-consuming finite-element (FE) model to alleviate the computational burden. DREAM essentially is a multichain sampling method that runs different paths to seek all possible solutions and accurately approximate the posterior probability distribution function in the Bayesian approach. The proposed updating framework was demonstrated using one numerical example and a real-world cable-stayed pedestrian bridge. The results showed that the proposed method enables rationally identifying structural parameters and recovering dynamic responses. Compared with the traditional Bayesian approach without a surrogate model, the computational cost is orders of magnitude lower.

Sparse-grids uncertainty quantification of part-scale additive manufacturing processes

The present paper aims at applying uncertainty quantification methodologies to process simulations of powder bed fusion of metal. In particular, for a part-scale thermomechanical model of an Inconel 625 super-alloy beam, we study the uncertainties of three process parameters, namely the activation temperature, the powder convection coefficient and the gas convection coefficient. First, we perform a variance-based global sensitivity analysis to study how each uncertain parameter contributes to the variability of the beam displacements. The results allow us to conclude that the gas convection coefficient has little impact and can therefore be fixed to a constant value for subsequent studies. Then, we conduct an inverse uncertainty quantification analysis, based on a Bayesian approach on synthetic displacement data, to quantify the uncertainties of the two remaining parameters, namely the activation temperature and the powder convection coefficient. Finally, we use the results of the inverse uncertainty quantification analysis to perform a data-informed forward uncertainty quantification analysis of the residual strains. Crucially, we make use of surrogate models based on sparse grids to keep to a minimum the computational burden of every step of the uncertainty quantification analysis. The proposed uncertainty quantification workflow allows us to substantially ease the typical trial-and-error approach used to calibrate power bed fusion part-scale models, and to greatly reduce uncertainties on the numerical prediction of the residual strains. In particular, we demonstrate the possibility of using displacement measurements to obtain a data-informed probability density function of the residual strains, a quantity much more complex to measure than displacements.