Parametric Quantification Research Articles

A Review Paper on Natural and Synthetic Refrigerants

The Montreal Protocol (1987) prohibited halogenated hydrocarbons with a high ozone depletion potential (ODP) because of their harmful effects on the ozone layer, which protects the earth from UV radiation. The greenhouse gases (GHG) utilized in contemporary refrigeration, air conditioning, and heat-pumping systems are subject to a time-limited permit term under the Kyoto Protocol (1997). The European Union law (2014) and the Paris Accord (2016) place a significant emphasis on the phase-out of hazardous synthetic refrigerants in order to prevent ozone depletion and reverse climate change impacts. The usage of natural refrigerants results in no net increase in greenhouse gas (GHG) emissions in the environment. Extensive research is being conducted globally to adapt and alter current cooling and heating systems utilizing natural refrigerants. This study uses the Refrigerant Qualitative Parametric (RQP) quantification model to examine timeworn, current, and next-generation refrigerants in order to aid the refrigerant selection process. It is calculated using the arithmetic sums of real refrigerant parametric values adjusted to corresponding ideal values. This model may aid in the selection of alternative refrigerants for temporary replacement of CFCs with HCFCs or HFCs, and eventual replacement of HCFCs or HFCs with low GWP and ODP synthetic and natural refrigerants.

Acute changes in mitral valve geometry after percutaneous valve repair with MitraClip XTR by three-dimensional echocardiography.

Mitral valve (MV) repair with MitraClip system is a safe treatment option for high-risk patients with significant mitral regurgitation (MR). We aimed to characterize, by three-dimensional echocardiography (3D-E), changes occurring in MV after implantation of third generation MitraClip XTR device, with specific reference to the underlying MR mechanism (functional vs degenerative, FMR vs DMR). We prospectively enrolled 59 patients, who underwent intra-procedural 3D-E before and after device deployment. Three-D datasets were analyzed off-line, using a dedicated semiautomatic software, to obtain parametric quantification of mitral anatomy. Post-procedural MR of mild or lesser degree was achieved in 40 patients (68%), with no differences between FMR and DMR (p 0.9). After MitraClip XTR implantation, the FMR group experienced an immediate annular resizing, with reduction of antero-posterior diameter (p 0.024) and sphericity index (p 0.017), next to a recovery of physiological saddle-shape, defined by lower non-planar angle (p ≤0.001) and higher annulus height to commissural width ratio (p ≤0.001). On the opposite, the DMR group revealed a significant decrease of maximum annular velocity (p 0.027), addressing a mechanic effect of the device deployment. Finally, baseline anterior mitral leaflet angle was found as an independent predictor of acute procedural result (OR 6.7, [CI 1.01-44.33], p 0.049). MitraClip XTR implantation acts in restoring the original mitral geometry, with distinctive effects according to MR mechanism. Three-D parametric quantification of MV sheds new light on changes occurring in the valvular apparatus, and helps identifying possible new predictors of acute procedural success.

Uncertainty analysis and stochastic characterization of carbon nanotube-based mass sensor with multiple deposited nanoparticles

Input uncertainties on the location, mass, and geometry of multiple deposited nanoparticles for carbon nanotube-based mass sensor are investigated. The carbon nanotube (CNT) is modeled as an Euler-Bernoulli beam with end constrained boundary conditions and Eringen’s nonlocal elasticity theory to account for size-dependent phenomena. Additionally, the displacement field of the CNT is broken up into components to the left and right of each deposited particle. Utilizing the Hamilton’s principle and the discretized displacement fields, the nonlocal governing equations of motion, boundary conditions, and continuity conditions at the deposited particle locations are derived. The effects of the particle location, mass, and geometry on the inherent frequency shifts before and after deposition are studied. Following these parametric studies, sensitivity analysis and uncertainty quantification methods are applied for two different nominal configurations of the mass sensor. The importance of the input parameters is deeply discussed, focusing especially on the location effects on the first and second natural frequency shifts. It is shown that increasing the mass and size of the particle increases the overall frequency shift, while varying the location of the particles does not strictly lead to increased frequency shifts. Finally, it is shown that due to the high number of input parameters, there are multiple particle configurations that lead to identical frequency shifts. These findings may be used by other researchers to extend the usability, usefulness, and characterization of mass detection devices.

A methodology for uncertainty quantification and sensitivity analysis for responses subject to Monte Carlo uncertainty with application to fuel plate characteristics in the ATRC

Large-scale reactor simulation often requires the use of Monte Carlo calculation techniques to estimate important reactor parameters. One drawback of these Monte Carlo calculation techniques is they inevitably result in some uncertainty in calculated quantities. The present study includes parametric uncertainty quantification (UQ) and sensitivity analysis (SA) on the Advanced Test Reactor Critical (ATRC) facility housed at Idaho National Laboratory (INL) and addresses some complications due to Monte Carlo uncertainty when performing these analyses. This approach for UQ/SA includes consideration of Monte Carlo code uncertainty in computed sensitivities, consideration of uncertainty from directly measured parameters and a comparison of results obtained from brute-force Monte Carlo UQ versus UQ obtained from a surrogate model. These methodologies are applied to the uncertainty and sensitivity of keff for two sets of uncertain parameters involving fuel plate geometry and fuel plate composition.Results indicate that the less computationally-expensive method for uncertainty quantification involving a linear surrogate model provides accurate estimations for keff uncertainty and the Monte Carlo uncertainty in calculated keff values can have a large effect on computed linear model parameters for parameters with low influence on keff.

Dynamic FDG-PET in localization of focal epilepsy: A pilot study

Epilepsy surgery remains underutilized, in part because non-invasive methods of potential seizure foci localization are inadequate. We used high-resolution, parametric quantification from dynamic 2-[18F] fluoro-2-deoxy-d-glucose positron emission tomography (dFDG-PET) imaging to locate hypometabolic foci in patients whose standard clinical static PET images were normal. We obtained dFDG-PET brain images with simultaneous EEG in a one-hour acquisition on seven patients with no MRI evidence of focal epilepsy to record uptake and focal radiation decay. Images were attenuation- and motion-corrected and co-registered with high-resolution T1-weighted patient MRI and segmented into 18 regions of interest (ROI) per hemisphere. Tracer uptake was calibrated with a model corrected blood input function with partial volume (PV) corrections to generate tracer parametric maps compared between mean radiation values between hemispheres with z-scores. We identified ROI with the lowest negative z scores (<−1.65 SD) as hypometabolic. Dynamic 2-[18F] fluoro-2-deoxy-d-glucose positron emission tomography ( found focal regions of altered metabolism in all cases in which standard clinical FDG-PET found no abnormalities. This pilot study of dynamic FDG-PET suggests that further research is merited to evaluate whether glucose dynamics offer improved clinical utility for localization of epileptic foci over standard static techniques.

Modeling neutronic transients with Galerkin projection onto a greedy-sampled, POD subspace

Presented here is an application of POD-Galerkin projection to develop a reduced-order-model (ROM) that approximates the solution of the multi-group, time-dependent, diffusion equation with a lower computational cost. Such reduced models are often sought in the context of parametric studies and uncertainty quantification, which require successive evaluation of the full-order model (FOM). To construct the ROM efficiently, greedy sampling was used to generate a reduced subspace that represents the entire parameter (here, cross-sections) domain. By using this subspace, the ROM is expected to yield accurate predictions when used in place of the FOM for uncertainty quantification conducted, e.g., with direct Monte-Carlo sampling. The TWIGL benchmark was used here for illustration. A ROM constructed with a POD basis of rank 10 was able to reproduce the core power with a maximum RMS error on the order of 10–6, and for the precursors concentration it was 10–9. Moreover, the statistical moments obtained from the ROM were in good agreement with those of the full-order-model. The mean relative error of the power sample mean prediction was about 4 ×10–6 for both the ramp and the step perturbations. In terms of the computational efficiency, the ROM time, including the projection, is approximately four-times faster than the full-order-model.

Nonintrusive uncertainty quantification for automotive crash problems with VPS/Pamcrash

Uncertainty Quantification (UQ) is a key discipline for computational modeling of complex systems, enhancing reliability of engineering simulations. In crashworthiness, having an accurate assessment of the behavior of the model uncertainty allows reducing the number of prototypes and associated costs. Carrying out UQ in this framework is especially challenging because it requires highly expensive simulations. In this context, surrogate models (metamodels) allow drastically reducing the computational cost of Monte Carlo process. Different techniques to describe the metamodel are considered, Ordinary Kriging, Polynomial Response Surfaces and a novel strategy (based on Proper Generalized Decomposition) denoted by Separated Response Surface (SRS). A large number of uncertain input parameters may jeopardize the efficiency of the metamodels. Thus, previous to define a metamodel, kernel Principal Component Analysis (kPCA) is found to be effective to simplify the model outcome description. A benchmark crash test is used to show the efficiency of combining metamodels with kPCA. • Nonintrusive combination of data techniques and surrogates for parametric analysis, design and uncertainty quantification. • Application to VPS/Pamcrash finite elements crashworthiness simulations for automotive industry. • A novel surrogate model, the Separated Response Surface (SRS), based on Proper Generalized Decomposition method. • Application on a benchmark crash model of interest for automotive industry (Volkswagen Group).

Open access tool and microfluidic devices for phenotypic quantification of heart function of intact fruit fly and zebrafish larvae

In this paper, the heartbeat parameters of small model organisms, i.e. Drosophila melanogaster (fruit fly) and Danio rerio (zebrafish), were quantified in-vivo in intact larvae using microfluidics and a novel MATLAB-based software. Among different developmental stages of flies and zebrafish, the larval stage is privileged due to biological maturity, optical accessibility, and the myogenic nature of the heart. Conventional methods for parametric quantification of heart activities are complex and mostly done on dissected, irreversibly immobilized, or anesthetized larvae. Microfluidics has helped with reversible immobilization without the need for anesthesia, but heart monitoring is still done manually due to challenges associated with the movement of floating organs and cardiac interruptions. In our MATLAB software applied to videos recorded in microfluidic-based whole-organism assays, we have used image segmentation to automatically detect the heart and extract the heartbeat signal based on pixel intensity variations of the most contractile region of the heart tube. The smoothness priors approach (SPA) was applied to remove the undesired low-frequency noises caused by environmental light changes or heart movement. Heart rate and arrhythmicity were automatically measured from the detrended heartbeat signal while other parameters including end-diastolic and end-systolic diameters, shortening distance, shortening time, fractional shortening, and shortening velocity were quantified for the first time in intact larvae, using M-mode images under bright field microscopy. The software was able to detect more than 94% of the heartbeats and the cardiac arrests in intact Drosophila larvae. Our user-friendly software enables in-vivo quantification of D. melanogaster and D. rerio larval heart functions in microfluidic devices, with the potential to be applied to other biological models and used for automatic screening of drugs and alleles that affect their heart.

Multi-objective Design and Optimization of Power Electronics Converters With Uncertainty Quantification—Part II: Model-Form Uncertainty

The second part of the multi-objective design and optimization with parametric and model-form uncertainty quantification (MDO with P&MF-UQ) is dedicated to incorporating MF-UQ into the MDO framework. MF-UQ is used to estimate the error due to modeling inaccuracies and to validate the mathematical models used in the MDO framework. In this approach, the sensitivity index introduced in the first part of the article is modified too so that it is a quantitative measure of system design robustness with regards to modeling inaccuracies as well as the manufacturing variability in the design of systems with multiple performance functions. The optimum design solution is finally realized by exploring the Pareto Front of the enhanced performance space, where the model-form error associated with each design is used to modify the estimated performance measures and the parametric sensitivity of each design point is considered to discern between cases and help identify the most parametrically robust of the Pareto-optimal design solutions. To demonstrate the benefits of incorporating uncertainty quantification analysis into the design optimization from a more practical standpoint, design of a robust high-efficiency high-power-density 1.25 kW Vienna-type rectifier is used as a case study to compare the theoretical analysis with a comprehensive experimental validation. It is shown that the final design selected using the MDO with P&MF-UQ reduces the design sensitivity and system loss by 33% and 5%, respectively, compared to the optimal design selected using the conventional MDO.

The impact of uncertainty on predictions of the CovidSim epidemiological code.

Epidemiological modelling has assisted in identifying interventions that reduce the impact of COVID-19. The UK government relied, in part, on the CovidSim model to guide its policy to contain the rapid spread of the COVID-19 pandemic during March and April 2020; however, CovidSim contains several sources of uncertainty that affect the quality of its predictions: parametric uncertainty, model structure uncertainty and scenario uncertainty. Here we report on parametric sensitivity analysis and uncertainty quantification of the code. From the 940 parameters used as input into CovidSim, we find a subset of 19 to which the code output is most sensitive-imperfect knowledge of these inputs is magnified in the outputs by up to 300%. The model displays substantial bias with respect to observed data, failing to describe validation data well. Quantifying parametric input uncertainty is therefore not sufficient: the effect of model structure and scenario uncertainty must also be properly understood.

Improved Modeling of Microwave Structures Using Performance-Driven Fully-Connected Regression Surrogate

Fast replacement models (or surrogates) have been widely applied in the recent years to accelerate simulation-driven design procedures in microwave engineering. The fundamental reason is a considerable—and often prohibitive—CPU cost of massive full-wave electromagnetic (EM) analyses related to solving common tasks such as parametric optimization or uncertainty quantification. The most popular class of surrogates are data-driven models, which are fast to evaluate, versatile, and easy to handle. Notwithstanding, the curse of dimensionality as well as the utility demands (e.g., so that the model covers sufficiently broad ranges of the system operating conditions), limit the applicability of conventional methods. A performance-driven modeling paradigm allows for mitigating these issue by focusing the surrogate setup process in a constrained domain encapsulating designs being of high quality w.r.t. the assumed figures of interest. The nested kriging framework capitalizing on this idea, renders the constrained surrogate using kriging interpolation, and has been shown to surpass traditional approaches. In pursuit of further accuracy improvements, this work incorporates the performance-driven concept into the fully-connected regression model (FRCM). The latter has been recently introduced in the context of frequency selective surfaces, and combined deep neural networks with Bayesian optimization, the latter employed to determine the network architecture and hyper-parameters. Using two examples of miniaturized microstrip couplers, our methodology is demonstrated to outperform both conventional modeling techniques and nested kriging, with reliable models constructed over multi-dimensional parameters spaces using just a few hundreds of samples.

Optimal design for kernel interpolation: Applications to uncertainty quantification

The paper is concerned with classic kernel interpolation methods, in addition to approximation methods that are augmented by gradient measurements. To apply kernel interpolation using radial basis functions (RBFs) in a stable way, we propose a type of quasi-optimal interpolation points, searching from a large set of candidate points, using a procedure similar to designing Fekete points or power function maximizing points that use pivot from a Cholesky decomposition. The proposed quasi-optimal points results in smaller condition number, and thus mitigates the instability of the interpolation procedure when the number of points becomes large. Applications to parametric uncertainty quantification are presented, and it is shown that the proposed interpolation method can outperform sparse grid methods in many interesting cases. We also demonstrate the new procedure can be applied to constructing gradient-enhanced Gaussian process emulators.

On the Modeling and Design of Modular Multilevel Converters With Parametric and Model-Form Uncertainty Quantification

Modeling and design with parametric and model-form uncertainty quantification is an alternative to conventional model-based design approaches as it improves the existing modeling practice and validates the model used in the design of power converters. However, in the case of modular multilevel converters (MMCs), uncertainty quantification, as the main step in this design methodology, becomes challenging due to the inherent complexity and sheer size of such units. In this article, these limitations are discussed and a systematic study for developing a simplified testbed for uncertainty quantification of an MMC is presented. To this end, first sensitivity analysis is conducted to identify the key parameters whose tolerances contribute the most to the parametric uncertainty of the selected design variables. Second, the effect of increasing the number of power cells in each arm on the estimated total uncertainty, and thus the predictive capability of the MMC simulation models for medium- and high-voltage applications is studied. A simplified testbed for model validation of the power cell in the design of an MMC is developed accordingly. The development of this simplified testbed allows validating the models used and estimating uncertainties in the design with less computational cost and hardware prototyping.

A Bayesian Logistic Regression for Probabilistic Forecasts of the Minimum September Arctic Sea Ice Cover

AbstractThis study introduces a Bayesian logistic regression framework that is capable of providing skillful probabilistic forecasts of Arctic sea ice cover, along with quantifying the attendant uncertainties. The presence or absence of ice (absence defined as ice concentration below 15%) is modeled using a categorical regression model, with atmospheric, oceanic, and sea ice covariates at 1‐ to 7‐month lead times. The model parameters are estimated in a Bayesian framework, thus enabling the posterior predictive probabilities of the minimum sea ice cover and parametric uncertainty quantification. The model is fitted and validated to September minimum sea ice cover data from 1980 through 2018. Results show overall skillful forecasts of the minimum sea ice cover at all lead times, with higher skills at shorter lead times, along with a direct measure of forecast uncertainty to aide in assessing the reliability.

Design-oriented modeling of antenna structures by means of two-level kriging with explicit dimensionality reduction

The employment of full-wave electromagnetic (EM) analysis is a practical necessity in the design of contemporary antenna structures. This is because simpler models are generally not available or of limited accuracy. At the same time, EM-based design is computationally expensive. Consequently, the ways of accelerating tasks such as parametric optimization or uncertainty quantification have to be sought. A possible workaround that has been gaining popularity over the recent years is utilization of fast surrogates. Among these, data-driven models are the most popular due to their versatility and easy handling. Notwithstanding, the curse of dimensionality and utility requirements (e.g., having the surrogate valid over broad ranges of geometry and operating parameters) limit the applicability of conventional approximation approaches to antenna modeling. Recently proposed performance-driven methods, especially the nested kriging framework, allow for going beyond the capability of the standard techniques. This is achieved by an appropriate confinement of the model domain, defined to contain only high-quality designs with respect to the selected performance figures. This paper proposes a novel approach, which combines the main idea of the nested kriging, specifically, the first-level model as a tool for constructing the domain-defining manifold, as well as principal component analysis to reduce the domain dimensionality in an explicit manner. Comprehensive benchmarking using three antenna structures indicates superiority of our methodology over conventional techniques, but also nested kriging, in terms of the achievable predictive power. The latter is obtained without compromising design utility of the model as demonstrated through application case studies.

Multi-objective Design and Optimization of Power Electronics Converters With Uncertainty Quantification—Part I: Parametric Uncertainty

This article presents a robust multi-objective design and optimization approach with parametric and model-form uncertainty quantification (MDO with P&MF-UQ). The first part of the article focuses on incorporating parametric uncertainty quantification (P-UQ) into the MDO framework, where a sensitivity index is defined as a quantitative measure of system design robustness with regards to manufacturing variability in the design of systems with multiple performance functions. To demonstrate the benefits of incorporating P-UQ analysis into the design optimization framework, this article presents the design and optimization of a robust high-efficiency high-power-density 1.25 kW Vienna-type rectifier. The optimum design solution is realized by exploring the Pareto Front of the enhanced performance space where the parametric sensitivity of each design point is considered to discern between cases and help identify the most parametrically-robust of the Pareto-optimal design solutions. It is shown that the design sensitivity is reduced by 39% when the optimum design is selected using MDO with P-UQ rather than the conventional MDO.

Effects of Photovoltaic Module Materials and Design on Module Deformation Under Load

Quasi-static structural finite-element models of an aluminum-framed crystalline silicon photovoltaic module and a glass-glass thin-film module were constructed and validated against experimental measurements of deflection under uniform pressure loading. Specific practices in the computational representation of module assembly were identified as influential to matching experimental deflection observations. Additionally, parametric analyses using Latin hypercube sampling were performed to propagate input uncertainties related to module materials, dimensions, and tolerances into uncertainties in simulated deflection. Sensitivity analyses were performed on the uncertainty quantification datasets using linear correlation coefficients and variance-based sensitivity indices to elucidate key parameters influencing module deformation. Results identified edge tape and adhesive material properties as being strongly correlated to module deflection, suggesting that optimization of these materials could yield module stiffness gains at par with the conventionally structural parameters, such as glass thickness. This exercise verifies the applicability of finite-element models for accurately predicting mechanical behavior of solar modules and demonstrates a workflow for model-based parametric uncertainty quantification and sensitivity analysis. Applications of this capability include the assessment of field environment loads, derivation of representative loading conditions for reduced-scale testing, and module design optimization, among others.

Reexamining the Mission Architecture Decision of Project Apollo: A New Parametric Perspective

Although the historical and technical details of Project Apollo have been extensively documented in literature, current records indicate that there is still a lack of an early-design-phase, physics-based, parametric sizing quantification of the engineering decisions that made Apollo a success. Historical texts that explain the design decisions of Apollo do so in a predominantly qualitative manner, leaving out the physics-based Future Projects Office–type calculations, whereas technical texts tend to explain the design details at higher fidelity, overall leading the engineer away from the big picture design understanding. This paper reexamines the critical mission architecture (or mission mode) decision from a holistic and parametric perspective. After parametrically connecting a launch vehicle sizing process with an in-space element sizing process, a generic mission architecture solution space is generated that enables the visualization and comparison of the various Project Apollo architecture options. The mission planner can then consistently compare the competing architecture options like lunar orbit rendezvous or direct flight with each other based on their overall launch mass, launch performance, and launch vehicle cost. It is identified that the lunar orbit rendezvous approach is the clear winner in terms of launch vehicle size and cost.

Koopman-Based Approach to Nonintrusive Reduced Order Modeling: Application to Aerodynamic Shape Optimization and Uncertainty Propagation

A methodology for nonintrusive projection-based nonlinear model reduction originally presented by Renganathan et al. (“Koopman-Based Approach to Nonintrusive Projection-Based Reduced-Order Modeling with Black-Box High-Fidelity Models,” AIAA Journal, Vol. 56, No. 10, 2018, pp. 4087–4111) is further extended toward parametric systems with a focus on application to aerospace design. Specifically, the method is extended to address static systems with parametric geometry (that deforms the mesh) in addition to parametric freestream boundary conditions. The main idea is to first perform a transformation on the governing equations such that it is lifted to a higher-dimensional but linear underdetermined system. This enables one to extract the system matrices easily as compared to that of the original nonlinear system. The underdetermined system is closed with a set of model-dependent nonlinear constraints upon which the model reduction is finally performed. The methodology is validated on the subsonic and transonic inviscid flows past the NACA0012 and the RAE2822 airfoils with parametrized shapes. The utility of the approach is further demonstrated by applying it to two common problems in aerospace design, namely, derivative-free global optimization and parametric uncertainty quantification with Monte Carlo sampling. Overall, the methodology is shown to achieve accuracy up to 5% and computational speedup of two to three orders of magnitude relative to the full order model. Comparison against another nonintrusive model reduction method revealed that the proposed approach is more robust, accurate, and retains the consistency between the state variables.

Parametric uncertainty quantification in natural frequency of sandwich plates using polynomial neural network

In this paper, uncertainty quantification in natural frequencies for laminated soft core sandwich plates is presented by employing finite element (FE) coupled polynomial neural network (PNN) approach. The computational efficiency and accuracy is achieved by using PNN as surrogate model. Latin hypercube sampling method is employed for training of data in PNN model. The stochastic first three natural frequencies of sandwich plates are studied for individual variation in input parameters. The stochasticity in individual input parameters are considered in order to assess their influence on global response of the structure. The algorithm discussed in this article is observed to be converging with the previously published literature (for deterministic case) and validated with full scale Monte Carlo simulation (MCS) i.e. original finite element approach (for stochastic case). The computational time and cost reduced significantly by employing the present surrogate based FE approach compared to that of conventional Monte Carlo simulation approach.