Sensitivity analysis and optimization of optical Y-branch structure parameters.

Parametric sensitivity analysis (SA) is an essential tool in optical data analysis aiming to quantify the relative importance of optical model parameters and identify those with a low influence which should remain fixed during analysis in order to simplify a model. Typically, such sensitivity studies are performed using a local sensitivity analysis, also referred to as “one-at-a-time” analysis, which estimates parameter sensitivity by evaluating the changes in model output while perturbing one parameter at a time and holding all other parameters fixed. All the pitfalls of the local sensitivity approach are quite obvious and well known; however, local SA is still prevailing in the area of data analysis for spectroscopic ellipsometry. In this study, we discuss applications of a global qualitative analysis introduced by Morris in 1991 which determines an overall significance for each model parameter and describes its nonlinear effect on model’s output and/or interactions with other parameters. The Morris method allows effective separation of the model parameters into different groups such as parameters with negligible effects, parameters with large linear effects without interactions, and parameters with large nonlinear and/or interaction effects. Here, we carried out the Morris sensitivity analysis to reveal the model parameter significance ranking in a test case of the B-spline model for titanium nitride (TiN). Such a screening approach can be considered as a practical tool for the initial global SA strategy prior to true “all-at-a-time” global sensitivity analysis.

Load modeling plays an important role in accessing and enhancing the dynamic stability of power systems. Though the Synthesis Load Model Considering Voltage Regulation of Distribution Network ( $\pi $ model) has high accuracy, its parameters are too many. In order to improve the identification efficiency and reduce the difficulty of identification, a simplified model identification strategy based on parameter sensitivity analysis is proposed. Firstly, based on the global sensitivity analysis, the sensitivity analysis of the model parameters is carried out to obtain the First Order Sensitivity Indices ( FSI )and Total Sensitivity Indices ( TSI ). Secondly, the FSI and TSI of each parameter are analyzed, and the effect on the output of model of each parameter is determined by FSI . For less influential parameters, whether the parameter should be fixed as constant is determined by the value of TSI . The parameter whose TSI equal or approximately equal to zero should be fixed as a constant. Finally, the improved genetic algorithm is used to identify the parameter-simplified model, and the effectiveness of the simplified identification strategy is verified by comparing the fitting effects with the measured curve and the residual and the integrated parameter models.

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

Comprehensive evaluation of parameter importance and optimization based on the integrated sensitivity analysis system: A case study of the BTOP model in the upper Min River Basin, China

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

Identifying key sources of uncertainty in the modelling of greenhouse gas emissions from wastewater treatment

Ecosystem models are useful tools for understanding ecological processes and for sustainable management of resources. In biogeochemical field, numerical models have been widely used for investigating carbon dynamics under global changes from site to regional and global scales. However, it is still challenging to optimize parameters and estimate parameterization uncertainty for complex process‐based models such as the Erosion Deposition Carbon Model (EDCM), a modified version of CENTURY, that consider carbon, water, and nutrient cycles of ecosystems. This study was designed to conduct the parameter identifiability, optimization, sensitivity, and uncertainty analysis of EDCM using our developed EDCM‐Auto, which incorporated a comprehensive R package—Flexible Modeling Framework (FME) and the Shuffled Complex Evolution (SCE) algorithm. Using a forest flux tower site as a case study, we implemented a comprehensive modeling analysis involving nine parameters and four target variables (carbon and water fluxes) with their corresponding measurements based on the eddy covariance technique. The local sensitivity analysis shows that the plant production‐related parameters (e.g., PPDF1 and PRDX) are most sensitive to the model cost function. Both SCE and FME are comparable and performed well in deriving the optimal parameter set with satisfactory simulations of target variables. Global sensitivity and uncertainty analysis indicate that the parameter uncertainty and the resulting output uncertainty can be quantified, and that the magnitude of parameter‐uncertainty effects depends on variables and seasons. This study also demonstrates that using the cutting‐edge R functions such as FME can be feasible and attractive for conducting comprehensive parameter analysis for ecosystem modeling.

Global Sensitivity Analysis of Arrhythmic Risk Biomarkers in Cardiac Single Cell Models

To enhance the accuracy of advanced constitutive models for soft natural clays, several parameters are necessary, resulting in complexity of numerical modelling. However, the detailed effects of these parameters are not rigorously quantified towards their constitutive relationships. Thus, the aim of the paper is to assess such advanced models in order to determine the most significant parameters over the time series data. Two methods for Global Sensitivity Analysis (GSA), i.e. Experimental Design and the Sobol method, were used and benchmarked to assess the model predictions on a discretised domain in time and space. A rate-dependent Finite Element model using Creep-SCLAY1S and a hydro-mechanically coupled formulation for consolidation was used to study a Constant Rate of Strain (CRS) test. The value of GSA approaches adopted herein was to investigate the model predictions both in the temporal and spatial domain. The temporal analyses indicate three sets of significant model parameters in different portions of the CRS compression curve. Furthermore, the non-stationary nature of sensitivity results is exposed, identifying the parameters that lead to unique solutions for the CRS loading path. The FE implementation enabled the quantification of the most sensitive model parameters in the spatial domain. The spatial results that are governed by the rate-dependent processes in the soil (i.e. consolidation and creep) illustrated that Experimental Design was capable of providing sensitivity maps with satisfactory accuracy similar to the Sobol method. Experimental Design was found to be the most efficient method, concerning execution time and storage costs, to assess rate-dependent problems in Geotechnics.

Parameter sensitivity analysis can determine the influence of the input parameters on the model output. Identification and calibration of critical parameters are the crucial points of the process model optimization. Based on the Extended Fourier Amplitude Sensitivity Test (EFAST) and the Morris method, this paper analyzes and compares the parameter sensitivity of the annual mean net primary productivity (NPP) of Larix olgensis Henry forests in Jilin Province simulated by the Lund–Potsdam–Jena dynamic global vegetation model (LPJ model) in 2009–2014 and 2000–2019, and deeply examines the sensitivity and influence of the two methods to each parameter and their respective influence on the model’s output. Moreover, it optimizes some selected parameters and re-simulates the NPP of Larix olgensis forests in Jilin Province from 2010 to 2019. The conclusions are the following: (1) For the LPJ model, the sensitive and non-influential parameters could be identified, which could guide the optimization order of the model and was valuable for model area applications. (2) The results of the two methods were similar but not identical. The sensitivity parameters were significantly correlated (p < 0.05); parameter krp was the most sensitive parameter, followed by parameters αm, αa and gm. These sensitive parameters were mainly found in the photosynthesis, water balance, and allometric growth modules. (3) The EFAST method had a higher precision than the Morris method, which could calculate quantitatively the contribution rate of each parameter to the variances of the model results; however, the Morris method involved fewer model running times and higher efficiency. (4) The mean relative error (MRE) and mean absolute error (MAE) of the simulated value of LPJ model after parameter optimization decreases. The optimized annual mean value of NPP from 2010 to 2019 was 580 g C m−2 a−1, with a mean annual growth rate of 2.13%, exhibiting a fluctuating growth trend. The MAE of the simulated value of LPJ model after parameter optimization decreases.

This paper presents the use of Global Sensitivity Analysis (GSA) methods to analyze the sensitivity level of the performance of the impedance measurement algorithm of SEL-421 distance relay protection when used to perform transmission line protection with compensation circuit. This GSA technique was developed to see the dominance effect of system uncertainty (or factors). Two techniques that might be used for sensitivity analysis using GSA are Quasi-Monte Carlo (QMC) and data sampling with Sobol technique. Experimental is done with DIgSILENT software to do modeling of the power system, simulation, and calculation of impedance and algorithm error. The testing is carried out automatically with the help of the developed algorithm using DPL (DIgSILENT Programming Language). SIMLAB software, in this case, (with Sobol technique) is applied to generate some non-linear factor data and analyze the output of variations in impedance measurement errors.

Non-Linear Partial-Least-Squares-based Polynomial Chaos Expansion (NLPLS-based PCE) approach for global sensitivity analysis of a High-Q Partially Air-Filled Pedestal Resonator Integrated in a Printed Circuit Board (PCB)

Sensitivity analyses are frequently used during the design of engineering systems to qualify and quantify the effect of parametric variation in the performance of a system. Two primary types of sensitivity analyses are generally used: local and global. Local analyses, generally involving derivative-based measures, have a significantly lower computational burden than global analyses but only provide measures of sensitivity around a nominal point. Global analyses, generally performed with a Monte Carlo sampling approach, and variation-based measures provide a complete description of sensitivity but incur a large computational burden and require information regarding the distributions of the design parameters in a concept. Local analyses are generally suited to the early stages of design when parametric information is limited, and a large number of concepts must be evaluated (necessitating a light computational burden). Global analyses are more suited to the later stages of design when more information about parametric distributions is available and fewer concepts are under consideration. Current derivative-based local approaches provide a different and incompatible set of measures than a global variation-based analysis. This makes a direct comparison of local to global measures ill posed. To reconcile local and global sensitivity analyses, a hybrid local variation-based sensitivity (HyVar) approach is presented. This approach has a similar computational burden to a local approach but produces measures or percentage contributions. The HyVar approach is directly comparable to global variation-based approaches. In this paper, the HyVar sensitivity analysis method is developed in the context of a functional based behavioral modeling framework. An example application of the method is presented along with a summary of results produced from a more comprehensive example.

In this paper, we study the dynamical effects of timely and delayed diagnosis on the spread of COVID-19 in Ghana during its initial phase by using reported data from March 12 to June 19, 2020. The estimated basic reproduction number, ℛ0, for the proposed model is 1.04. One of the main focus of this study is global stability results. Theoretically and numerically, we show that the disease persistence depends on ℛ0. We carry out a local and global sensitivity analysis. The local sensitivity analysis shows that the most positive sensitive parameter is the recruitment rate, followed by the relative transmissibility rate from the infectious with delayed diagnosis to the susceptible individuals. And that the most negative sensitive parameters are: self-quarantined, waiting time of the infectious for delayed diagnosis and the proportion of the infectious with timely diagnosis. The global sensitivity analysis using the partial rank correlation coefficient confirms the directional flow of the local sensitivity analysis. For public health benefit, our analysis suggests that, a reduction in the inflow of new individuals into the country or a reduction in the inter community inflow of individuals will reduce the basic reproduction number and thereby reduce the number of secondary infections (multiple peaks of the infection). Other recommendations for controlling the disease from the proposed model are provided in Section 7.

In general design and analysis of a tunnel boring machine (TBM), many analytical models are proposed to predict the TBM's performance. Various models may result in different performance predictions for the same TBM excavating under the same geological conditions. Therefore, it is essential to perform the quantitative analysis of the impacts from different prediction models and the corresponding key input factors on the TBM's performance. Recently, there is almost no relevant study on such issues for TBM and it is urgent to fill this gap. In this paper, by comparing and analyzing the TBM's performance using different prediction models, three types of total thrust prediction models (the rapid-growth type, the intermediate type, and the slow-growth type) and two types of total torque prediction models (the rapid-growth type and the slow-growth type) are classified and defined for the first time in the TBM-related fields. Then, a global sensitivity analysis (SA) of TBM's performance using the Sobol' method is developed regarding key input factors, including control, structural, and geological parameters. It is found that the relative impacts of the input factors to TBM's performance vary appreciably with the selection of prediction models. Specifically, a global SA on the minimized construction period of a tunneling project with respect to structure parameters is performed. The results show that the structure parameters have similar impacts on the minimized construction period irrespective of the selection of prediction models. The impacts of different prediction models on the minimized construction period of a tunneling project using Genetic Algorithm (GA) are investigated by finding the optimal control and structure parameters. The results interestingly show that the selection of the TBM's performance prediction models has a marginal impact on the minimized construction period but yields partly different key parameters.