Local Sensitivity Method Research Articles

Comparison of local and global sensitivity analysis methods and application to thermal hydraulic phenomena

The best estimate plus uncertainty analysis have been widely applied for the safety assessment of nuclear systems, and sensitivity analysis is one of the essential steps to identify and rank the important phenomena and parameters. The conventionally used local sensitivity methods are based on linear hypothesis and have limitations in the application process of nonlinear systems, while the more complicated global sensitivity methods may have problem in time costs. To compare and propose the proper method for evaluation of thermal-hydraulic calculation in a reactor system, local methods such as Pearson correlation coefficient, Spearman rank correlation coefficient, and Kendall rank correlation coefficient, global methods such as the variance-based method, moment-independent method, and elementary effects method are reviewed and applied for numerical examples and specific reactor thermal-hydraulic problem in this paper. Results show that the rank of parameter importance measured by various local analysis methods is the same, but away from the global methods. Different types of global sensitivity analysis methods have similar results for parameters with higher importance, and among these methods, the elementary effects method has the lowest computational cost with the same number of samples.

Sensitivity analysis and optimization of PCM integrated buildings in a tropical savanna climate

Several researchers have reported the importance of early design stage decisions in the building design process. Integrating phase change material (PCM) in buildings is a feasible method for enhancing energy efficiency. However, the following issues have not been addressed yet. (a) What is the most effective combination of early design stage parameters that minimizes the energy consumption of PCM integrated residential buildings? (b) Can the various sensitivity analysis methods generate a similar ranking of early design stage parameters? (c) Can the same set of early design stage parameters be used for tropical savanna climates? (d) Are the optimal solutions economically and environmentally feasible? Hence, this research proposes a multi-stage sensitivity and optimization of the PCM incorporated buildings in tropical savanna climates by considering building layout, envelope thermal characteristics, and energy efficiency measures. For multi-stage sensitivity analysis, at the first stage, global sensitivity methods (Morris, standard rank regression coefficients, partial rank correlation coefficients) were used followed by the utilization of the local sensitivity method. An evolutionary algorithm was used to optimize the key early design stage parameters. Finally, the economic and environmental analysis was performed on optimal solutions. Results showed that all methods generated a different ranking of the importance of early design stage parameters. Due to optimization, the annual energy use decreased by about 18.2–42.7% in comparison to the base case. In addition, the optimal solutions are economically and environmentally pronounced. It is concluded that early design stage parameter selection is crucial in reducing building energy consumption.

Sensitivity Analysis Strategy to Assess the Salting-Out Problem during CO2 Geological Storage Process

The sensitivity analysis of the salting-out effect on well injectivity is a significant work in the research of geological storage of CO2 in deep saline aquifers, which is helpful in the selection of storage sites and the design of the injection strategy. We conduct a detailed sensitivity analysis about the salting-out process using the local sensitivity method and two global sensitivity methods. Sensitivity coefficients showed that brine salinity (XNaCl) has the highest sensitivity and interaction effect, the CO2 injection rate (QCO2) has a greater influence in the early stage of the salting-out process and a smaller influence in the end stage, and the other three parameters (empirical parameters related to the pore distribution m, the liquid residual saturation in the relative permeability function Splr, and the liquid residual saturation in the capillary pressure function Sclr) have a smaller sensitivity. This paper also analyzes the calculation amount of different sensitivity methods and suitable ways of obtaining the sensitivity coefficient and reveals the following. (1) The sensitivity coefficient changes dynamically with time, if only the sensitivity of the final state is taken into account on a long-time physical process, and some sensitive parameters during the process may be neglected. (2) The selection of the sample size should be based on the convergence of multiple calculations, and the results of the empirical calculation are uncertain. (3) The calculation of Sobol sensitivity is complicated, the results calculated by surrogate model depend on whether the sample is representative enough; on the other hand, it is feasible to use Sti-Si approximation to characterize the second-order sensitivity to reduce the computation. The research results not only reveal the sensitivity of the parameters related to the injection well salting-out problem during CO2 storage in deep saline aquifers but also guide the calculation of global sensitivity analysis with a similar physical process.

Aeronautical relay health state assessment model based on belief rule base with attribute reliability

Health state assessment is a key issue in health management of aeronautical relay subject to complex interference environment. The input reliability of assessment model has direct connection with the assessment result and the reliability of the assessment model. Due to the limitation of resources and monitoring technology, it is impossible to simultaneously improve the reliabilities of all the characteristics. Thus, some important characteristics should be sorted by the role they play in the assessment model. Implementing the quantitatively analysis of the influence of the input reliability can provide guidance. The belief rule base model with attribute reliability (BRB-r) provides such a modeling framework and analysis method. It is one of the expert systems that can aggregate unreliable quantitative data and expert knowledge and has traceability between the model input and output. Thus, in this paper, a new health state assessment model based on BRB-r for aeronautical relay is developed for the first time where the calculation method of model reliability is further developed. Then, to quantitatively analyze the effectiveness of the input reliability on the model output and the model reliability, the sensitivity analysis of attribute reliability is deduced based on the first-order local sensitivity method. The obtained sensitivity coefficient of attribute reliability represents its effectiveness on the constructed health state assessment model and can provide guidance in health management for aeronautical relay under limited resource. A case study of health sate estimation of the JRC-7M aeronautical relay is conducted to illustrate the application of the new model.

Sensitivity analysis on imaging the calcaneus using microwaves

The bone quality is associated with changes in its dielectric properties (permittivity and conductivity). The feasibility of detecting changes in these properties was evaluated by using a tomographic array of 16 monopole antennas with z-polarized microwaves at 1.3 GHz. The direct electromagnetic problem was solved computationally with the finite–difference–time–domain (FDTD) method. Local and global sensitivity analyses were implemented for identifying the parameters that most affect the detection. Magnitude and phase of the transmission coefficient of the antennas were evaluated separately. It was observed that the direct problem is highly sensitive to the dielectric properties of the tissues surrounding the calcaneus and to those of the calcaneus itself. Global and local sensitivity methods have shown evidence for feasible detection of variations in dielectric properties of the bone supporting the simplification of considering only two homogeneous media (calcaneus and surrounding tissue).

Numerical Simulation and Sensitivity Analysis for Nitrogen Dynamics Under Sewage Water Irrigation with Organic Carbon

This study is focused on investigating the impacts of organic carbon on the denitrification process of nitrogen transformation and transport. A numerical model, Nitrogen-2D, is modified by considering the impact of organic carbon in the denitrification equation. The modified model is used to simulate the soil nitrogen (including nitrate and ammonium) dynamics under the primary and secondary sewage water irrigation with different organic carbon concentrations. The simulated results of accumulated drainage water amount, soil nitrogen concentration, and nitrogen concentration in the drainage water show that the simulations and measurements are consistent. The comparison of results from the original and improved models shows the necessity to consider the impact of organic carbon. The nitrogen mass balance is calculated to analyze the nitrogen transformation processes quantitatively under different input organic carbon sources. Furthermore, the effect of different input organic carbon sources on the soil nitrogen dynamics is investigated by using the modified Nitrogen-2D model with the calibrated parameters. The input organic carbon source helps to speed up the mineralization and denitrification, which contributes to the slight increase of ammonium concentration and the decrease of nitrate concentration in the shallow soil. Since a large number of soil water and nitrogen transformation and transport parameters are needed when setting up the model, a local sensitivity method is conducted to evaluate the input parameters by the sewage water irrigation case. The results show that the drainage water amount is very sensitive to the exponent n and the coefficient α of the soil water retention function and that the ammonium concentration is very sensitive to the first-order nitrification rate constant, the decomposition rate coefficient in humus pool, and the soil ammonium adsorption coefficient. The nitrate concentration is sensitive to more parameters, especially to the exponent n and the coefficient α in the soil water retention function and to the denitrification rate constant.

A comparative design study and analysis of inner and outer rotor permanent magnet synchronous machine for power generation in vertical axis wind turbine using GSA and GSA-PSO

In wind energy conversion system, an electric generator is coupled with a wind turbine. The wind turbine is either vertical axis or horizontal axis wind turbine. To increase the efficiency the gear driven generator has been replaced by directly driven generator. This paper recounts the design optimization of inner and outer rotor permanent magnet synchronous machine of rating 500KVA, 3.3kV, 3-phase, and 600rpm. The weight of the generator has been taken as an objective function. The gravitational search algorithm and its hybridization with particle swarm optimization have been used as tools for optimization. The temperature rise, efficiency, regulation and maximum flux density in stator teeth are taken as constraints for design problem. The results of both types of generator configurations are obtained and compared. It is found that the efficiency of outer rotor permanent magnet synchronous generator is improved by 2.19% and regulation by 2.83% as compared to inner rotor permanent magnet synchronous generator. Lower temperature rise as 22.61°C is observed for outer rotor permanent magnet synchronous generator whereas it is 31.18°C in case of outer rotor permanent magnet synchronous machine. Further, the sensitivity analysis has been performed over design parameters using local sensitivity method for both generators.

Application of canonical correlation analysis to a sensitivity study of constitutive model parameter fitting

Successful modeling of a material's deformation behavior is dependent on the development of realistic constitutive models that can mimic the actual response of the material of interest. In-depth knowledge about the parameters in a constitutive model will lead to a better understanding of the relationship between flow stress and deformation conditions and will eventually aid in better design of the deformation process. Curve-fitting is generally employed to calibrate constitutive models using experimental data. However, the relative impact of constitutive model parameters on the mechanical response for different models has not been extensively explored. In this study, both local and global sensitivity analysis methods are used to understand and quantify the contribution of the parameters. Canonical correlation analysis (CCA) has been used to understand the effect of constitutive model parameters on the flow stress behavior of titanium alloys. This analysis has been performed for the Mechanical Threshold Stress (MTS) model, which is a constitutive description based on the physics of dislocation motion. The limitations of local sensitivity methods have been highlighted and it has been shown that CCA provides a measure of both an individual variable's contribution and the effectiveness of the parameter set as a whole.

Dynamic Analysis of a Predator and Prey Model with some Computational Simulations

Mathematical modelling and numerical simulations of interaction populations are crucial topics in systems biology. The interactions of ecological models may occur among individuals of the same species or individuals of different species. Describing the dynamics of such models occasionally requires some techniques of model analysis. Choosing appropriate techniques of model analysis is often a difficult task. We define a prey (mouse) and predator (cat) model. The system is modelled by a pair of non-linear ordinary differential equations using mass action law, under constant rates. A proper scaling is suggested to minimize the number of parameters. More interestingly, we propose a homotopy technique with n expanding parame- ters for finding some analytical approximate solutions. Furthermore, using the local sensitivity method is another important step forward in this study because it helps to identify critical model parameters. Numerical simulations are provided using Matlab for different parameters and initial conditions.

BitHash: An efficient bitwise Locality Sensitive Hashing method with applications

Locality Sensitive Hashing has been applied to detecting near-duplicate images, videos and web documents. In this paper we present a Bitwise Locality Sensitive method by using only one bit per hash value (BitHash), the storage space for storing hash values is significantly reduced, and the estimator can be computed much faster. The method provides an unbiased estimate of pairwise Jaccard similarity, and the estimator is a linear function of Hamming distance, which is very simple. We rigorously analyze the variance of One-Bit Min-Hash (BitHash), showing that for high Jaccard similarity. BitHash may provide accurate estimation, and as the pairwise Jaccard similarity increases, the variance ratio of BitHash over the original min-hash decreases. Furthermore, BitHash compresses each data sample into a compact binary hash code while preserving the pairwise similarity of the original data. The binary code can be used as a compressed and informative representation in replacement of the original data for subsequent processing. For example, it can be naturally integrated with a classifier like SVM. We apply BitHash to two typical applications, near-duplicate image detection and sentiment analysis. Experiments on real user’s photo collection and a popular sentiment analysis data set show that, the classification accuracy of our proposed method for two applications could approach the state-of-the-art method, while BitHash only requires a significantly smaller storage space.

Sensitivity analysis of the early‐age cracking risk in an immersed tunnel

AbstractEngineers know only too well that early‐age cracking accounts for the decrease of long‐term serviceability for a majority of infrastructure. In immersed tunnels, early‐age cracks may leave paths for aggressive media, which lead to deterioration and thus compromise durability. On the other hand, the cracking risk in concrete structures depends on a number of factors, such as material properties, construction methods, curing measures, etc., which make decisions complex.This work presents the results of a sensitivity analysis of early‐age behaviour for an immersed tunnel cast in situ. Numerical modelling and local sensitivity methods are employed to evaluate the sensitivity of early‐age cracking to casting temperature, formwork conductivity, formwork removal time, curing temperature and ambient temperature. The numerical results indicate that the casting and curing temperatures appear to be the most dominant factors with regard to the whole fabrication period.This study provides a realistic method for determining the uncertainty analysis of concrete structures at an early age, and identifies the most important factors during the fabrication of immersed tunnel segments, which is beneficial for further decisions related to the control of early‐age cracking.

Modeling the performance of large-scale CO2 storage systems: A comparison of different sensitivity analysis methods

In this study, we perform sensitivity analyses using a high-resolution basin-scale reservoir model developed for a hypothetical carbon sequestration project located in the Southern San Joaquin Basin in California, USA. We use the massively parallel version of the multiphase multicomponent simulator TOUGH2 to simulate CO2/brine migration and pressure buildup within the CO2 storage formation and overlying/underlying formations. We evaluate the impact of parameter uncertainty on risk-related performance measures, i.e., CO2 saturation and pressure buildup at multiple locations, and the extent of the CO2 plume and overpressure zone. We compare three sensitivity analysis methods: a local sensitivity method and the global Morris and Sobol’/Saltelli methods. The uncertainty of sensitivity indices in the global methods is evaluated so that we can interpret the results even when we have a limitation in the computational resources. Results show that the three methods provide complementary information for identifying important parameters and system understanding. All three methods give consistent interpretations and importance rankings, except when a parameter has a significant non-linear effect and/or strong interaction with some other parameters. In addition to the magnitude of parameter sensitivity, our analysis emphasizes the direction (i.e., favorable or adverse in the risk perspective), non-linearity and/or interaction effects, and physical interpretation of each parameter sensitivity trend. Parameter importance varies with time and space, and also depends on the CO2 plume or pressure behaviors. In this study, the reservoir permeability is among the most important parameters for all measures, although it has a large trade-off effect in risk such that a higher permeability would tend to reduce reservoir pressure but, at the same time, increase the size of the CO2 plume footprint.

Measuring the impact of nonignorability in panel data with non‐monotone nonresponse

SUMMARYThe analysis of panel data with non‐monotone nonresponse often relies on the critical and untestable assumption ofignorablemissingness. It is important to assess the consequences of departures from the ignorability assumption. Non‐monotone nonresponse, however, can often make such sensitivity analysis infeasible because the likelihood functions for alternative models involve high‐dimensional and difficult‐to‐evaluate integrals with respect to missing outcomes. We develop an extension of the local sensitivity method that overcomes computational difficulty and completely avoids fitting alternative models and evaluating these high‐dimensional integrals. The proposed method is applicable to a wide range of panel outcomes. We apply the method to a Smoking Trend dataset where we relax the standard ignorability assumption and evaluate how smoking‐trend estimates in different groups of US young adults are affected by alternative assumptions about the missing‐data mechanism. The main finding is that the standard estimate in the black male group is sensitive to nonignorable missingness but those in other groups are reasonably robust. Copyright © 2010 John Wiley & Sons, Ltd.

Sensitivity analysis and automatic calibration of a rainfall–runoff model using multi-objectives

The development of numerical model parameter sensitivity analysis (SA) has focused mainly on the selection of a single-objective measure of the distance between the model-simulated output and the data. However, practical experience with sensitivity analysis suggests that no single objective function is adequate to measure the ways in which the model fails to match the important characteristics of the observed data. In order to successfully measure parameter sensitivity of a numerical model, multiple criteria should be considered. Sensitivity analysis of a rainfall–runoff model is performed using the local sensitivity method (Morris method) and multi- objective analysis. Formulation of SA strategy for the MIKE/NAM rainfall–runoff model is outline. The SA scheme includes multiple objectives that measure different aspects of the hydrograph: (1) overall influence, and (2) parameter interaction. The SA is given as a set of Pareto ranks from a multi-objective viewpoint. In order to successfully calibrate the numerical model, multiple criteria should be considered. Multi-objective Differential Evolution (MODE) has proved effective in numerous such applications, where most of the techniques relying on the condition of Pareto efficiency to compare different solutions. We describe the performance of the population-based search algorithm (Non-dominated Sorting Differential Evolution (NSDE)) when applied to the rainfall–runoff model. The method has been applied for calibration of a test catchment and compared on validation data. The simulations show that the NSDE method possesses the ability to finding the optimal Pareto front and keeping a good diversity in the obtained front for the model calibration.