Sampling-based Sensitivity Analysis Research Articles

Surrogate-based worst-case analysis of a knee joint model using Genetic Algorithm

Verification, validation, and uncertainty quantification is generally recognized as a standard for assessing the credibility of mechanical models. This is especially evident in biomechanics, with intricate models, such as knee joint models, and highly subjective acquisition of parameters. Propagation of uncertainty is numerically expensive but required to evaluate the model reliability. An alternative to this is to analyze the worst-case models obtained within the specific bounds set on the parameters. The main idea of the paper is to search for two models with the greatest different response in terms of displacement-load curve. Real-Coded Genetic Algorithm is employed to effectively explore the high-dimensional space of uncertain parameters of a 2D dynamic knee model, while Radial Basis Function surrogates reduce the computation by orders of magnitude to near real-time, with negligible impact on the quality. It is expected that the studied knee joint model is very sensitive to uncertainty in the geometrical parameters. The obtained worst-case knee models showcase unrealistic behavior with one of them unable to fully extend, and the other largely overextending. Their relative difference in extension is up to 35% under ±1 mm bound set on the geometry. This unrealistic behavior of knee joint model is confirmed by the large standard deviation obtained from a classical sampling-based sensitivity analysis. The results confirm the viability of the method in assessing the reliability of biomechanical models. The proposed approach is general and could be applied to other mechanical systems as well.

Development, verification and application of the uncertainty analysis platform CUSA

Modeling and simulation technology has gradually become an important approach to describe objective physical phenomena and carry out further research and design. However, uncertainty in the basic input of the modeling and simulation process there naturally exists, which will inevitably propagate to the simulation results. Due to the wide applicability and easy implementation, statistical sampling-based Sensitivity and Uncertainty (SU) analysis has become the mainstream option for uncertainty propagation and quantification analysis in the modeling and simulation process. This paper first establishes a statistical sampling-based framework and gives theories and implemented methods involved in our framework in detail. Based on these theories and methods, a user-friendly and functional SU analysis platform called CUSA with a Human Machine Interface (HMI) has been developed. The verification results of the main function and basic theory prove the correctness and stability of CUSA. Finally, this paper summarizes CUSA's representative applications in previous studies and conduct the uncertainty analysis of total neutron physics calculation for a mini-core using CUSA.

A Sampling-Based Sensitivity Analysis Method Considering the Uncertainties of Input Variables and Their Distribution Parameters

For engineering products with uncertain input variables and distribution parameters, a sampling-based sensitivity analysis methodology was investigated to efficiently determine the influences of these uncertainties. In the calculation of the sensitivity indices, the nonlinear degrees of the performance function in the subintervals were greatly reduced by using the integral whole domain segmentation method, while the mean and variance of the performance function were calculated using the unscented transformation method. Compared with the traditional Monte Carlo simulation method, the loop number and sampling number in every loop were decreased by using the multiplication approximation and Gaussian integration methods. The proposed algorithm also reduced the calculation complexity by reusing the sample points in the calculation of two sensitivity indices to measure the influence of input variables and their distribution parameters. The accuracy and efficiency of the proposed algorithm were verified with three numerical examples and one engineering example.

New Strategies in the Code of Uncertainty and Sensitivity Analysis (CUSA) and Its Application in the Nuclear Reactor Calculation

Best-Estimation Plus Uncertainty (BEPU) analysis method can provide more information to improve the reliability of calculation results than the safety analysis with conservative assumption. And the statistical sampling-based uncertainty and sensitivity analysis methods are widely used in practical applications of the multiphysics, multiscale coupling nuclear reactor system. In this paper, a novel and efficient sampling method for inputs with normal and uniform distributions is introduced and a systematic theory for uncertainty and sensitivity analysis is established based on the classical statistical theory. Then the Code of Uncertainty and Sensitivity Analysis (CUSA) is updated based on these new strategies. For applications, the explicit and implicit effects for resonance and nonresonance isotopes are studied in depth, and a simple UO2 pin cell is considered to examine the performance of CUSA and the total uncertainty and sensitivity analysis abilities. The numerical results indicate that the implicit sensitivity analysis model and the uncertainty quantification functions developed in CUSA are correct and can be used for sensitivity and uncertainty analysis in nuclear reactor calculations. Even more important, the LHS-SVDC is recommended to propagate the uncertainties in multigroup cross sections.

Sensitivity analysis of complex engineering systems: Approaches study and their application to vehicle restraint system crash simulation

Restricted by high calculation cost of single engineering model run and large number of model runs for sampling-based Sensitivity Analysis (SA), qualitative SA are used for parameter study of the Vehicle Restraint System (VRS) and quantitative SA of such models has always been a challenge. Sequential approaches are proposed for SA of complex systems and the SA of a VRS is realized: sampling-based SA methods are discussed; SA of a simple three points dynamic bending test model is realized, the aims are to compare different two-level screening methods and put into practice the sequential SA; crash test FE model of a VRS is created and used for SA; influential uncertain parameters of the VRS are identified qualitatively through screening analyses (SA with Two-level screening and Morris Analysis), and Sobol’ indices are used to quantify the influence of influential parameters with Kriging metamodeling. The uncertain parameters which contribute the most to robustness of the VRS are identified and their influences are quantified by combining screening analyses and Sobol’ Indices.

Sensitivity and Uncertainty Analysis of a Fire Spread Model with Correlated Inputs

Abstract Sensitivity and uncertainty analysis is a very important tool to identify and treat model uncertainties in quantitative fire risk analysis. An existing Fire Spread model with correlated input variables are presented for sampling-based sensitivity analysis, and selected input variables include fire growth rate, fire resistance rating and its standard deviation, fire load density and its standard deviation. A sampling approach is proposed to deal with the correlated structure of input variables, which introduces a noise term and can transform correlated input variable structure into an independent one. Furthermore, sensitivity analysis of input variables of fire spread model is performed and an order of variable sensitivity is given. Results show that fire resistance rating and its standard deviation are two very important input variables while standard deviation of fire load density is the least sensitive parameter. Further discussions are provided on the effectiveness of the sampling technique and the use the results of the analysis.

The formation of continuous opinion dynamics based on a gambling mechanism and its sensitivity analysis

The formation of continuous opinion dynamics is investigated based on a virtual gambling mechanism where agents fight for a limited resource. We propose a model with agents holding opinions between and 1. Agents are segregated into two cliques according to the sign of their opinions. Local communication happens only when the opinion distance between corresponding agents is no larger than a pre-defined confidence threshold. Theoretical analysis regarding special cases provides a deep understanding of the roles of both the resource allocation parameter and confidence threshold in the formation of opinion dynamics. For a sparse network, the evolution of opinion dynamics is negligible in the region of low confidence threshold when the mindless agents are absent. Numerical results also imply that, in the presence of economic agents, high confidence threshold is required for apparent clustering of agents in opinion. Moreover, a consensus state is generated only when the following three conditions are satisfied simultaneously: mindless agents are absent, the resource is concentrated in one clique, and confidence threshold tends to a critical value(; , the average number of friends of individual agents). For fixed a confidence threshold and resource allocation parameter, the most chaotic steady state of the dynamics happens when the fraction of mindless agents is about 0.7. It is also demonstrated that economic agents are more likely to win at gambling, compared to mindless ones. Finally, the importance of three involved parameters in establishing the uncertainty of model response is quantified in terms of Latin hypercube sampling-based sensitivity analysis.

Assessing how uncertainty and stochasticity affect the dispersal of fish in river networks

Species dispersal and population dynamics determine the spatio-temporal patterns of species spread and thus, species invasions and recolonization following habitat restorations. However, the effects of stochasticity and spatial habitat heterogeneity on species spread are poorly understood.By coupling a fish dispersal model and a population growth model in GIS, we simulated the spread of a model fish species (Salmo trutta) over five years in river networks of varying habitat heterogeneity. Replicated model runs and a sampling-based sensitivity analysis allowed us to disentangle the uncertainty in the rate of spread related to (i) specific model input parameters and (ii) stochasticity inherent to the dispersal process.Our results revealed the spread of the model species being particularly sensitive to the choice of parameters determining fish dispersal (e.g. fish size) and less to demographic parameters (e.g. reproductive rate). Moreover, the spread of fish is strongly affected by stochasticity inherent to dispersal and the availability and spatial arrangement of suitable habitats patches. Stochastic effects cause considerable variations in the predictability of up to 120% of the median dispersal distance whereof 52% is solely attributed to stochasticity inherent to dispersal decisions.Our findings demonstrate that process-based models combining individual dispersal, population dynamics and spatial habitat heterogeneity as well as carefully selected model input parameters are crucial for reasonably simulating the spread of fishes in river networks. Moreover, we suggest considering stochasticity inherent to dispersal in models of species spread as this contributes to a considerable variation in the predictability of movement distances.

Building Energy Assessment Based on a Sequential Sensitivity Analysis Approach

Sensitivity analysis has been widely used in building energy assessment to provide reliable analysis of importance ranking for input variables in buildings. Most of previous studies used one single batch simulation models to obtain sensitivity indicators. To conduct robust analysis, this paper implements a sequential sensitivity analysis to assess the convergence of sensitivity indicators for two global sampling-based sensitivity analysis methods (standardized regression coefficients and meta-modelling Sobol) in an office building. The results indicate that this sequential method can be more effective and robust. In contrast, a single batch sensitivity method for building energy assessment may lead to non-convergence results due to smaller number of simulation models or over-convergence results due to larger number of simulation models. It is also found that the convergence rate for standardized regression methods are slower than that for the meta-modelling Sobol method.

Classification of hydrological parameter sensitivity and evaluation of parameter transferability across 431 US MOPEX basins

Summary The Community Land Model (CLM) represents physical, chemical, and biological processes of the terrestrial ecosystems that interact with climate across a range of spatial and temporal scales. As CLM includes numerous sub-models and associated parameters, the high-dimensional parameter space presents a formidable challenge for quantifying uncertainty and improving Earth system predictions needed to assess environmental changes and risks. This study aims to evaluate the potential of transferring hydrologic model parameters in CLM through sensitivity analyses and classification across watersheds from the Model Parameter Estimation Experiment (MOPEX) in the United States. The sensitivity of CLM-simulated water and energy fluxes to hydrological parameters across 431 MOPEX basins are first examined using an efficient stochastic sampling-based sensitivity analysis approach. Linear, interaction, and high-order nonlinear impacts are all identified via statistical tests and stepwise backward removal parameter screening. The basins are then classified according to their parameter sensitivity patterns (internal attributes), as well as their hydrologic indices/attributes (external hydrologic factors) separately, using Principal component analysis (PCA) and expectation–maximization (EM) – based clustering approach. Similarities and differences among the parameter sensitivity-based classification system (S-Class), the hydrologic indices-based classification (H-Class), and the Koppen climate classification systems (K-Class) are discussed. Within each parameter sensitivity-based classification system (S-Class) with similar parameter sensitivity characteristics, similar inversion modeling setups can be used for parameter calibration, and the parameters and their contribution or significance to water and energy cycling may also be more transferrable. This classification study provides guidance on identifiable parameters, and on parameterization and inverse model design for CLM but the methodology is applicable to other models. A set of experiments of model calibration were conducted to evaluate the transferability of model calibration strategies and parameter values within and between the classes. It was demonstrated that inverting parameters at representative sites belonging to the same class can significantly reduce parameter calibration efforts.

A proposal on accuracy estimation method for the sampling-based uncertainty analysis with Monte Carlo simulation technique

The sampling-based uncertainty analysis method is a stochastic approach to estimate response uncertainties caused by the uncertainty in the input parameters. Conventionally, to minimize the effects caused by the Monte Carlo stochastic uncertainty, lots of particle histories have been used for the uncertainty analysis. However, this can cause inefficiencies in the uncertainty analysis. To optimize the calculation efficiency, how the Monte Carlo stochastic uncertainty influences the response uncertainty should be clearly verified. In this study, a method to estimate the accuracy of the response uncertainty is proposed by introducing a standard error and an error propagation theory. Using the proposed method, response uncertainties and standard errors of the multiplication factors for three benchmark problems are evaluated by the Monte Carlo method. Our results show that the proposed method can accurately estimate the accuracy of the response uncertainty caused by the input uncertainty in using the Monte Carlo simulation method. The proposed method can be directly utilized to estimate the accuracy of the sampling-based uncertainty analysis using the Monte Carlo simulation method. Also, it is expected that the proposed method will contribute to an increase in the calculation efficiency in the sampling-based sensitivity and uncertainty analysis.

Competitive comparison of optimal designs of experiments for sampling-based sensitivity analysis

A widely used strategy to explore the sensitivity of the model to its inputs is based on a finite set of simulations. These are usually performed for a chosen set of points in a parameter space. An estimate of the sensitivity can be then obtained by computing correlations between the model inputs and outputs. The accuracy of the sensitivity prediction depends on a quality of the points distribution in the parameter space, so-called the design of experiments. The aim of the presented paper is to review and compare available criteria determining an optimal design of experiments for sampling-based sensitivity analysis.

Safety Analysis of Flow Parameters in a Rotor-stator Cavity

In order to ensure the safety of engine life limited parts (ELLP) according to airworthiness regulations, a numerical approach integrating one-way fluid structure interaction (FSI) and probabilistic risk assessment (PRA) is developed, by which the variation of flow parameters in a rotor-stator cavity on the safety of gas turbine disks is investigated. The results indicate that the flow parameters affect the probability of fracture of a gas turbine disk since they can change the distribution of stress and temperature of the disk. The failure probability of the disk rises with increasing rotation Reynolds number and Chebyshev number, but descends with increasing inlet Reynolds number. In addition, a sampling based sensitivity analysis with finite difference method is conducted to determine the sensitivities of the safety with respect to the flow parameters. The sensitivity estimates show that the rotation Reynolds number is the dominant variable in safety analysis of a rotor-stator cavity among the flow parameters.

A sensitivity analysis of the New Zealand standard model of foot and mouth disease

Disease simulation models can be a valuable tool for planning a response to exotic disease incursions, as they provide a fast, low-cost mechanism for identifying the likely outcomes of a range of outbreak scenarios and disease control strategies. To use these tools effectively and with confidence, decision-makers must understand the simplifications and framing assumptions that underlie a model's structure. Sensitivity analysis, the analytical process of identifying which input variables are the key drivers of the model's output, is a crucial process in developing this understanding. This paper describes the application of a sampling-based sensitivity analysis to the New Zealand standard model (NZSM). This model is a parameter set developed for the InterSpread Plus model platform to allow the exploration of different outbreak scenarios for an epidemic of foot and mouth disease in New Zealand. Based on 200 iterations of the NZSM, run for a simulation period of 60 days, settings related to farm-to-saleyard movements and the detection of disease during the active surveillance phase of the epidemic had the greatest influence on the predicted number of infected premises. A small number of counter-intuitive findings indicated areas of model design, implementation and/or parameterisation that should be investigated further. A potentially useful result from this work would be information to aid the grouping or elimination of non-influential model settings. This would go some way towards reducing the overall complexity of the NZSM, while still allowing it to remain fit for purpose.

Safety Analysis of Flow Parameters in a Rotor-Stator Cavity

In order to ensure the safety of engine life limited parts according to airworthiness regulations, a numerical method integrating one-way fluid structure interaction and probabilistic risk assessment is developed, by which the variation of flow parameters in a rotor-stator cavity on the safety of gas turbine disks is investigated. The results indicate that the flow parameters affect the probability of fracture of a gas turbine disk since they can change the distribution of stress and temperature of the disk. The failure probability of the disk rises with increasing rotation Reynolds number and Chebyshev number, but descends with increasing inlet Reynolds number. In addition, a sampling based sensitivity analysis with finite difference method is conducted to determine the sensitivities of the safety with respect to the flow parameters. The sensitivity estimates show that the rotation Reynolds number is the dominant variable in safety analysis of a rotor-stator cavity among the flow parameters.

Exploring a minimal two-component p53 model

The tumor suppressor p53 coordinates many attributes of cellular processes via interlocked feedback loops. To understand the biological implications of feedback loops in a p53 system, a two-component model which encompasses essential feedback loops was constructed and further explored. Diverse bifurcation properties, such as bistability and oscillation, emerge by manipulating the feedback strength. The p53-mediated MDM2 induction dictates the bifurcation patterns. We first identified irradiation dichotomy in p53 models and further proposed that bistability and oscillation can behave in a coordinated manner. Further sensitivity analysis revealed that p53 basal production and MDM2-mediated p53 degradation, which are central to cellular control, are most sensitive processes. Also, we identified that the much more significant variations in amplitude of p53 pulses observed in experiments can be derived from overall amplitude parameter sensitivity. The combined approach with bifurcation analysis, stochastic simulation and sampling-based sensitivity analysis not only gives crucial insights into the dynamics of the p53 system, but also creates a fertile ground for understanding the regulatory patterns of other biological networks.

Global sensitivity analysis in wastewater treatment plant model applications: Prioritizing sources of uncertainty

This study demonstrates the usefulness of global sensitivity analysis in wastewater treatment plant (WWTP) design to prioritize sources of uncertainty and quantify their impact on performance criteria. The study, which is performed with the Benchmark Simulation Model no. 1 plant design, complements a previous paper on input uncertainty characterisation and propagation (Sin et al., 2009). A sampling-based sensitivity analysis is conducted to compute standardized regression coefficients. It was found that this method is able to decompose satisfactorily the variance of plant performance criteria (with R2 > 0.9) for effluent concentrations, sludge production and energy demand. This high extent of linearity means that the plant performance criteria can be described as linear functions of the model inputs under the defined plant conditions. In effect, the system of coupled ordinary differential equations can be replaced by multivariate linear models, which can be used as surrogate models. The importance ranking based on the sensitivity measures demonstrates that the most influential factors involve ash content and influent inert particulate COD among others, largely responsible for the uncertainty in predicting sludge production and effluent ammonium concentration. While these results were in agreement with process knowledge, the added value is that the global sensitivity methods can quantify the contribution of the variance of significant parameters, e.g., ash content explains 70% of the variance in sludge production. Further the importance of formulating appropriate sensitivity analysis scenarios that match the purpose of the model application needs to be highlighted. Overall, the global sensitivity analysis proved a powerful tool for explaining and quantifying uncertainties as well as providing insight into devising useful ways for reducing uncertainties in the plant performance. This information can help engineers design robust WWTP plants.

Proper orthogonal decomposition and cluster weighted modeling for sensitivity analysis of sound propagation in the atmospheric surface layer

Outdoor sound propagation predictions are compromised by uncertainty and error in the atmosphere and terrain representations, and sometimes also by simplified or incorrect physics. A model's predictive power, i.e., its accurate representation of the sound propagation, cannot be assessed without first quantifying the ensemble sound pressure variability and sensitivity to uncertainties in the model's governing parameters. This paper describes fundamental steps toward this goal for a single-frequency point source. The atmospheric surface layer is represented through Monin-Obukhov similarity theory and the acoustic ground properties with a relaxation model. Sound propagation is predicted with the parabolic equation method. Governing parameters are modeled as independent random variables across physically reasonable ranges. Latin hypercube sampling and proper orthogonal decomposition (POD) are employed in conjunction with cluster-weighted models to develop compact representations of the sound pressure random field. Full-field sensitivity of the sound pressure field is computed via the sensitivities of the POD mode coefficients to the system parameters. Ensemble statistics of the full-field sensitivities are computed to illustrate their relative importance at every down range location. The central role of sensitivity analysis in uncertainty quantification of outdoor sound propagation is discussed and pitfalls of sampling-based sensitivity analysis for outdoor sound propagation are described.

Evaluation of Sampling-Based Methods for Sensitivity Analysis: Case Study for the E. coli Food Safety Process Risk Model

ABSTRACT This article evaluates selected sensitivity analysis methods applicable to risk assessment models with two-dimensional probabilistic frameworks, using a microbial food safety process risk model as a test-bed. Six sampling-based sensitivity analysis methods were evaluated including Pearson and Spearman correlation, sample and rank linear regression, and sample and rank stepwise regression. In a two-dimensional risk model, the identification of key controllable inputs that can be priorities for risk management can be confounded by uncertainty. However, despite uncertainty, results show that key inputs can be distinguished from those that are unimportant, and inputs can be grouped into categories of similar levels of importance. All selected methods are capable of identifying unimportant inputs, which is helpful in that efforts to collect data to improve the assessment or to focus risk management strategies can be prioritized elsewhere. Rank-based methods provided more robust insights with respect to the key sources of variability in that they produced narrower ranges of uncertainty for sensitivity results and more clear distinctions when comparing the importance of inputs or groups of inputs. Regression-based methods have advantages over correlation approaches because they can be configured to provide insight regarding interactions and nonlinearities in the model.

Sensitivity analysis in conjunction with evidence theory representations of epistemic uncertainty

Three applications of sampling-based sensitivity analysis in conjunction with evidence theory representations for epistemic uncertainty in model inputs are described: (i) an initial exploratory analysis to assess model behavior and provide insights for additional analysis; (ii) a stepwise analysis showing the incremental effects of uncertain variables on complementary cumulative belief functions and complementary cumulative plausibility functions; and (iii) a summary analysis showing a spectrum of variance-based sensitivity analysis results that derive from probability spaces that are consistent with the evidence space under consideration.