Simple Parametric Model Research Articles

Waterjet Modeling to Calculate High Speed Vessels’ Performance

Similar to the matching process between the main engine and propeller in a conventional vessel, there is a basic necessity to match main engine and waterjet in a high speed craft. Unlike the ability of the naval architect to review the overall impact of the engine and propeller selection in terms of thrust, delivered power, fuel consumption and vessel range, when coming to match a waterjet to a particular vessel, the performance data presented by the waterjet manufacturers is in some ways simplistic and does not contribute to the naval architect's effort to assess the complete performance picture of the propulsion system. In this article, a simple parametric modeling of the waterjet is presented which is common to all waterjets and enables the naval architect to match and assess the interaction between main engine and waterjet much like the process when matching main engine to a propeller. It will be shown that the constant power lines for thrust and rotational speed of a waterjet can in fact be consolidated into a single nondimensional set of curves similar to the nondimensional KT/KQ/ηo of a conventional propeller. This process will allow in fact the overall assessment of the matching problem between the main engine and the waterjet. Some waterjet manufacturers provide data for different impeller designs in which case this process can provide the naval architect a tool to choose the optimal impeller. Unlike the graphical nature of the performance assessment of the conventional data presented by the waterjet manufacturers, this method of modeling allows the digital/analytical solution in any intermediate speed and power setting. For the sake of simplicity, this article does not deal with the cavitation phenomena and the loss of thrust when the waterjet is cavitating although these are important issues that should be considered when assessing waterjet performance.

Order Protection through Delayed Messaging

Several financial exchanges recently introduced messaging delays (e.g. IEX and NYSE American) to protect ordinary investors from high-frequency traders who exploit stale orders. To capture the impact of such delays, we propose a simple parametric model of the continuous double auction market format. The model shows how messaging delays can lower transactions costs but typically increase queuing costs. Recently available field data support two key predictions: the distribution of queued pegged orders is highly leptokurtotic (discrete Laplace), and opportunities to profit from dynamic choice of pegged vs market orders are small and fleeting.

Magnifying the ATLAS stealth stop splinter: impact of spin correlations and finite widths

In this paper, we recast a “stealth stop” search in the notoriously difficult region of the stop-neutralino Simplified Model parameter space for which mleft({tilde{t}}_1right)-mleft({tilde{upchi}}_1^0right)simeq {m}_t . The properties of the final state are nearly identical for tops and stops, while the rate for stop pair production is mathcal{O} (10%) of that for toverline{t} . Stop searches away from this stealth region have left behind a “splinter” of open parameter space when mleft({tilde{t}}_1right)simeq {m}_t . Removing this splinter requires surgical precision: the ATLAS constraint on stop pair production reinterpreted here treats the signal as a contaminant to the measurement of the top pair production cross section using data from sqrt{s}=7 TeV and 8 TeV in a correlated way to control for some systematic errors. ATLAS fixed mleft({tilde{t}}_1right)simeq {m}_tkern0.5em andkern0.5em mleft({tilde{upchi}}_1^0right)=1 GeV, implying that a careful recasting of these results into the full mleft({tilde{t}}_1right)-mleft({tilde{upchi}}_1^0right) plane is warranted. We find that the parameter space with mleft({tilde{upchi}}_1^0right)lesssim 55 GeV is excluded for mleft({tilde{t}}_1right)simeq {m}_t — although this search does cover new parameter space, it is unable to fully pull the splinter. Along the way, we review a variety of interesting physical issues in detail: (i) when the two-body width is a good approximation; (ii) how assuming the narrow width approximation affects the total rate; (iii ) how the production rate is affected when the wrong widths are used; (iv ) what role propagating the spin correlations consistently through the multi-body decay chain plays in the limits. In addition, we provide a guide to using MadGraph for implementing the full production including finite width and spin correlation effects, and we survey a variety of pitfalls one might encounter.

Modeling Tangential Vector Fields on a Sphere

ABSTRACTPhysical processes that manifest as tangential vector fields on a sphere are common in geophysical and environmental sciences. These naturally occurring vector fields are often subject to physical constraints, such as being curl-free or divergence-free. We start with constructing parametric models for curl-free and divergence-free vector fields that are tangential to the unit sphere through applying the surface gradient or the surface curl operator to a scalar random potential field on the unit sphere. Using the Helmholtz–Hodge decomposition, we then construct a class of simple but flexible parametric models for general tangential vector fields, which are represented as a sum of a curl-free and a divergence-free components. We propose a likelihood-based parameter estimation procedure, and show that fast computation is possible even for large datasets when the observations are on a regular latitude–longitude grid. Characteristics and practical utility of the proposed methodology are illustrated through extensive simulation studies and an application to a dataset of ocean surface wind velocities collected by satellite-based scatterometers. We also compare our model with a bivariate Matérn model and a non-stationary bivariate global model. Supplementary materials for this article are available online.

Strengthened infilled RC frames: Continuum and macro modeling in nonlinear finite element analysis

Abstract Strengthening and retrofitting masonry infill Reinforced Concrete (RC) frames is crucial due to the large use of this structural typology in earthquake-prone countries. Masonry infills can provide a positive and negative effect on the seismic response. A positive effect is due to the fact that the infills dissipate energy and therefore increase the overall damping. A negative effect may take place if their disposition is irregular or if they fail irregularly, thus the structure behavior becomes irregular. Furthermore, the infills generally stiffen the structure and thus increase the base shear force. It has been shown that by using an adequate infill strengthening technique, performance and safety of the structures and of the infills can be improved. Several models for Un-Reinforced Masonry (URM) infills have been developed in the past, but there is a lack of models available to describe the behavior of strengthened infilled frames. A simplified analytical strut and tie model is proposed based on the results obtained by Finite Element (FE) analyses. The mechanical characteristics of the tension tie and of the compression strut depend on the stiffness and strength of the reinforcement in addition to the geometrical and mechanical parameters of the infilled frame. The proposed model is validated with experimental results of a Carbon Fiber Reinforced Polymer (CFRP) strengthened infilled RC frame. The experimental data are reproduced by means of continuum FE models in order to assess the influence of various parameters on the seismic response and to calibrate the simplified model's parameters. Lateral stiffness and strength obtained with this simplified model show a good agreement with the experimental results and the continuum FE models.

Predicting pulsar scintillation from refractive plasma sheets

The dynamic and secondary spectra of many pulsars show evidence for long-lived, aligned images of the pulsar that are stationary on a thin scattering sheet. One explanation for this phenomenon considers the effects of wave crests along sheets in the ionized interstellar medium, such as those due to Alfv\'en waves propagating along current sheets. If these sheets are closely aligned to our line-of-sight to the pulsar, high bending angles arise at the wave crests and a selection effect causes alignment of images produced at different crests, similar to grazing reflection off of a lake. Using geometric optics, we develop a simple parameterized model of these corrugated sheets that can be constrained with a single observation and that makes observable predictions for variations in the scintillation of the pulsar over time and frequency. This model reveals qualitative differences between lensing from overdense and underdense corrugated sheets: Only if the sheet is overdense compared to the surrounding interstellar medium can the lensed images be brighter than the line-of-sight image to the pulsar, and the faint lensed images are closer to the pulsar at higher frequencies if the sheet is underdense, but at lower frequencies if the sheet is overdense.

A simple parametric model observer for quality assurance in computer tomography

Model observers are mathematical classifiers that are used for the quality assessment of imaging systems such as computer tomography. The quality of the imaging system is quantified by means of the performance of a selected model observer. For binary classification tasks, the performance of the model observer is defined by the area under its ROC curve (AUC). Typically, the AUC is estimated by applying the model observer to a large set of training and test data. However, the recording of these large data sets is not always practical for routine quality assurance.In this paper we propose as an alternative a parametric model observer that is based on a simple phantom, and we provide a Bayesian estimation of its AUC. It is shown that a limited number of repeatedly recorded images (10–15) is already sufficient to obtain results suitable for the quality assessment of an imaging system. A MATLAB® function is provided for the calculation of the results.The performance of the proposed model observer is compared to that of the established channelized Hotelling observer and the nonprewhitening matched filter for simulated images as well as for images obtained from a low-contrast phantom on an x-ray tomography scanner. The results suggest that the proposed parametric model observer, along with its Bayesian treatment, can provide an efficient, practical alternative for the quality assessment of CT imaging systems.

A study to investigate viscous coupling effects on the hydraulic conductance of fluid layers in two-phase flow at the pore level

This paper examines the role of momentum transfer across fluid-fluid interfaces in two-phase flow. A volume-of-fluid finite-volume numerical method is used to solve the Navier-Stokes equations for two-phase flow at the micro-scale. The model is applied to investigate viscous coupling effects as a function of the viscosity ratio, the wetting phase saturation and the wettability, for different fluid configurations in simple pore geometries. It is shown that viscous coupling effects can be significant for certain pore geometries such as oil layers sandwiched between water in the corner of mixed wettability capillaries. A simple parametric model is then presented to estimate general mobility terms as a function of geometric properties and viscosity ratio. Finally, the model is validated by comparison with the mobilities computed using direct numerical simulation.

A fast and simple model to estimate the contribution of the circumsolar irradiance to measured broadband beam irradiance under cloud-free conditions in desert environment

Routine measurements of the broadband beam irradiance at normal incidence by means of pyrheliometers or equivalent pyranometric systems include unknown contributions from the irradiance originating from within the extent of the solar disc Bnsun, and that from a larger circumsolar region defined by its solid angle aperture, called the circumsolar normal irradiance CSn. This article describes a fast and simple parametric model that estimates the beam and circumsolar radiation, for opening half-angles in the interval [0.4°, 5°], under cloud-free conditions in a desert environment. 1 min measurements of the beam normal Bn, global G and diffuse D horizontal irradiances at Solar Village, Saudi Arabia, and Tamanrasset, Algeria, were used for calibration and validation. Using AERONET measurements as inputs to the radiative transfer code libRadtran, it has been checked–through an ‘indirect’ validation with the ground measured Bn–that the modelled Bnsun and CSn are accurate. Accordingly, a library of Bnsun and CSn modelled by libRadtran for varying solid angle apertures was generated. Building on this library, a fast parametric model was developed to estimate Bnsun and CSn using G, D and Bn as inputs. The coefficients of the model were fitted to a training set of measurements and then validated twice: once at their respective site, and once at the other site. When using the coefficients for their own site for both Solar Village and Tamanrasset for CSn, the relative bias is respectively −2.7% and −1.5%, the relative root mean square error (RMSE) is 19.9% and 19.6%, and the correlation coefficient is 0.871 and 0.935. As for Bnsun, the relative bias is −2.0% and −2.2%, the RMSE is 2.7% and 3.6%, and the correlation coefficient is 0.999 and 0.998. Applying the coefficients of one site to the other site yields satisfactory results. It is recommended to use the coefficients of Tamanrasset for desert sites exhibiting frequent clear skies, and those of Solar Village for sites exhibiting frequent turbid skies. The coefficients have also been fitted using data from both sites, for a combined model.

Evaluation of a synthetic rainfall model, P-CLIPER, for use in coastal flood modeling

With the projected increase in both tropical cyclone (TC) intensity and proportion of the global population living near the coast, adequate preparation to protect against TC flooding is in the economic interest of coastal cities worldwide. Numerical models that describe TC properties, e.g., storm surge and wind fields, are currently employed to simulate the component of flooding that results from seawater inundation of areas along the coast (i.e., saltwater flooding). However, without the inclusion of freshwater flooding, contributed by inland surface flow and direct precipitation, a total water level (TWL) system for TC flooding lacks a complete picture of the actual coastal flood levels. Working toward a true TWL system, this research investigates the efficacy of the simple and efficient parametric TC rainfall model P-CLIPER (PDF Precipitation-Climatology and Persistence) to provide historically representative TC rainfall to a TWL system. This research demonstrates the success of this novel use of P-CLIPER through calibration and validation to the Tar–Pamlico River and Neuse River coastal watershed in North Carolina. In particular, the comparison of hydrographs at observation stations shows that hydrologic model output forced with P-CLIPER matches that forced with radar-observed precipitation for both timing and peaks, with the proper parameter choices for P-CLIPER. Similarly with proper parameter selection, P-CLIPER captures the peak rate and spatial pattern of observed rainfall for Hurricane Isabel. Due to the model’s simplicity, this work also reveals that P-CLIPER can be used as a parametric rainfall model in ensemble simulations, which could lead toward improved floodplain mapping, emergency management decisions, and stormwater infrastructure planning.

Mitigating Complex Dust Foregrounds in Future Cosmic Microwave Background Polarization Experiments

Abstract Polarized Galactic foregrounds are one of the primary sources of systematic error in measurements of the B-mode polarization of the cosmic microwave background (CMB). Experiments are becoming increasingly sensitive to complexities in the foreground frequency spectra that are not captured by standard parametric models, potentially affecting our ability to efficiently separate out these components. Employing a suite of dust models encompassing a variety of physical effects, we simulate observations of a future seven-band CMB experiment to assess the impact of these complexities on parametric component separation. We identify configurations of frequency bands that minimize the “model errors” caused by fitting simple parametric models to more complex “true” foreground spectra, which bias the inferred CMB signal. We find that: (a) fits employing a simple two-parameter modified blackbody (MBB) dust model tend to produce significant bias in the recovered polarized CMB signal in the presence of physically realistic dust foregrounds; (b) generalized MBB models with three additional parameters reduce this bias in most cases, but non-negligible biases can remain, and can be hard to detect; (c) line-of-sight effects, which give rise to frequency decorrelation, and the presence of iron grains are the most problematic complexities in the dust emission for recovering the true CMB signal. More sophisticated simulations will be needed to demonstrate that future CMB experiments can successfully mitigate these more physically realistic dust foregrounds.

A semiparametric approach to evaluate the harm of low-dose exposures

While moderate to high levels of radiation exposure is known to cause adverse health effects, there is still controversy about the lowest dose that could be harmful. Given that epidemiological studies of practical sizes are unlikely to provide sufficient statistical power to detect a small risk in the low-dose range of concern, greater emphasis should be given to evaluating low-dose risk uncertainty. Using simulations under various dose–response relationships with a threshold, we show that a conventional approach based on simple parametric models (e.g. the linear model with or without a threshold) can be inefficient, biased and/or inaccurate in uncertainty evaluations at low doses. Alternatively, we consider a Bayesian semiparametric model of a connected piecewise-linear function allowing for autocorrelations between adjacent line sections. With no specific assumption, this can describe various plausible dose–response curves while appropriately handling the risk uncertainty. In particular, it can relatively accurately evaluate the dose range in which a threshold might exist, while retaining statistical power for a small risk increase after the threshold. As an illustration, we analyse cancer incidence data of Japanese atomic bomb survivors, a primary epidemiological source of quantitative risk estimates for health effects from radiation exposure.

Multi-Objective Simulation-Optimization Model for Long-term Reservoir Operation using Piecewise Linear Hedging Rule

An efficiently parameterized and appropriately structured piecewise linear hedging rule is formulated and included within a multi-objective simulation-optimization (S-O) framework that seeks to obtain Pareto-optimal solutions for the long-term hedged operation of a single water supply reservoir. Two conflicting objectives, namely, “minimize the total shortage ratio” and “minimize the maximum shortage” are considered in the S-O framework, while explicit specification of constraints is avoided in the optimization module. Evolutionary search based non-dominated sorting genetic algorithm is used as the driver, which is linked to the simulation engine that invokes the piecewise linear hedging rule within the S-O framework. Preconditioning of the multi-objective stochastic search of the time-varying piecewise linear hedging model is effected by feeding initial feasible solutions sampled from the Pareto-optimal front of a simple constant hedging parameter model, which has resulted in significant improvement of the Pareto-optimality and the computational efficiency.

Tree-Based Methods for Clustering Time Series Using Domain-Relevant Attributes

We propose a set of two new methods for clustering time series that captures temporal information (trend, seasonality and autocorrelation) and domain-relevant cross-sectional attributes. The methods are based on model-based partitioning (MOB) trees and can be used as an automated yet transparent tool for clustering a large collection of time series. The single-step method clusters series using trend, seasonality, time series lags and domain-relevant cross-sectional attributes, using a single linear regression model. The two-step method first clusters by trend, seasonality and domain-relevant cross-sectional attributes, and then further clusters the residuals series by autocorrelation and the domain-relevant crosssectional attributes. Both methods produce clusters that are interpretable by domain experts. We illustrate the usefulness of the proposed clustering approach by considering one-step-ahead forecasting. We present empirical results of comparing our approach to forecasting each series using an Auto Regressive Integrated Moving Average (ARIMA) model applied to a large set of Wikipedia article pageviews time series. Our results show that the tree-based approach produces forecasts that are practically on par with ARIMA models, yet are significantly faster and more efficient, thereby suitable for scaling to large collections of time-series. Moreover, our method produces simple parametric forecasting models for interpretable clusters of time series, whereas ARIMA cannot provide such interpretability.

Estimation window strategies for value-at-risk and expected shortfall forecasting

Compared with the large number of value-at-risk (VaR) and expected shortfall (ES) forecasting models proposed in the literature, few contributions have been made to address the question of which estimation window strategy is preferable for forecasting these risk measures. To fill this gap, we apply different estimation window strategies to a set of simple parametric, semiparametric and nonparametric industry-standard risk models. Analyzing daily return data on constituents of the German Deutscher Aktienindex (DAX), we evaluate forecasts by backtesting the unconditional coverage and independent and identically distributed properties of VaR violations, the ES forecasting accuracy and the conditional predictive ability. We thereby demonstrate that the selection of the estimation window strategy leads to significant performance differences. The results indicate that forecast combinations are the preferable estimation window strategy.

Optimal synthesis of the low-order model parameters for a large-scale energy system on the basis of the gramians spectral decomposition

Abstract The structure of the low-order model is characterized by the fact the eigenvalues of its dynamics matrix coincide with the weakly stable eigenvalues of the system, which are calculated using the spectrum of the system dynamics matrix and the method of the gramians spectral decompositions. The optimal synthesis of the simplified model parameters is based on the approximate solution of the matrix polynomial equation for the matrices of the numerator of the system matrix transfer function and its simplified model. The solution of the synthesis problem leads to the solution of the linear matrix algebraic equation formed by the adaptability matrices. The energy functionals of the system and its simplified model can be determined by means of spectral decompositions of the squared H2 -norm of the matrix transfer function of the system and its simplified model. When the system approaches to the stability boundary, the stability margins of the system and its simplified model determined by the dominant weakly stable eigenvalues coincide asymptotically. This makes it possible not only to guarantee the stability of the simplified model, but also to determine the stability margins of a high-order system with help of the stability margins of a low-order model. The method makes it possible to estimate the oscillational instability caused by the resonant interaction of intraregional and inter-area oscillations and also to evaluate the impact of the input and output system matrices on the system stability using input and output matrices of its simplified model.

Generic distortion model for metrology under optical microscopes

For metrology under optical microscopes, lens distortion is the dominant source of error. Previous distortion models and correction methods mostly rely on the assumption that parametric distortion models require a priori knowledge of the microscopes’ lens systems. However, because of the numerous optical elements in a microscope, distortions can be hardly represented by a simple parametric model. In this paper, a generic distortion model considering both symmetric and asymmetric distortions is developed. Such a model is obtained by using radial basis functions (RBFs) to interpolate the radius and distortion values of symmetric distortions (image coordinates and distortion rays for asymmetric distortions). An accurate and easy to implement distortion correction method is presented. With the proposed approach, quantitative measurement with better accuracy can be achieved, such as in Digital Image Correlation for deformation measurement when used with an optical microscope. The proposed technique is verified by both synthetic and real data experiments.

A novel correction for biases in forest eddy covariance carbon balance

Systematic biases in eddy covariance measurements of net ecosystem-atmosphere carbon dioxide exchange (NEE) are ubiquitous in forests when turbulence is low at night. We propose an alternative to the conventional bias correction, the friction velocity (u*) filter, by hypothesizing that these biases have two separate, concurrent causes: (1) a subcanopy CO2 storage pool that eludes typical storage measurements, creating a turbulence-dependent bias, and (2) advective divergence loss of CO2, creating a turbulence-independent bias. We correct for (1) using a simple parametric model of missing storage (MS). Prior experiments have inferred (2) directly from atmospheric measurements (DRAINO). For sites at which DRAINO experiments have not been performed or are infeasible, we estimate (2) empirically using a PAR-extrapolated advective respiration loss (PEARL) approach. We compare u* filter estimates of advection and NEE to MS-PEARL estimates at one temperate forest and two tropical forest sites.We find that for tropical forests, u* filters can produce a range of extreme NEE estimates, from long-term forest carbon emission to sequestration, that diverge from independent assessments and are not physically sustainable. Our MS model eliminates the dependence of nighttime NEE on u*, consistent with findings from DRAINO studies that nighttime advective losses of CO2 are often not dependent on the strength of turbulence. Our PEARL estimates of mean advective loss agree with available DRAINO measurements. The MS-PEARL correction to long-term NEE produces better agreement with forest inventories at all three sites. Moreover, the correction retains all nighttime eddy covariance data and is therefore more widely applicable than the u* filter approach, which rejects substantial nighttime data—up to 93% at one of the tropical sites. The full MS-PEARL NEE correction is therefore an equally defensible and more practical alternative to the u* filter, but leads to different conclusions about the resulting carbon balance. Our results therefore highlight the need to investigate which approach’s underlying hypotheses are more physically realistic.

A gamma process modeling approach for the comparison of dissolution profiles

In this paper, we propose a stochastic gamma process model for assessing the similarity of two dissolution profiles. Based on the proposed stochastic model, we utilize the difference factor and similarity factor to test the similarity of two dissolution profiles based on bootstrap confidence intervals. The performances of the proposed methods are compared with a multivariate test procedure via Monte Carlo simulation studies. The proposed testing methods are shown to be powerful and effectively controlling the error rate. The proposed model provides a simple yet useful alternative parametric statistical model for assessing the similarity of two dissolution profiles. All the methods are illustrated with a numerical example.

Parametric modeling and optimal experimental designs for estimating isobolograms for drug interactions in toxicology

ABSTRACTIn toxicology and related areas, interaction effects between two substances are commonly expressed through a combination index evaluated separately at different effect levels and mixture ratios. Often, these indices are combined into a graphical representation, the isobologram. Instead of estimating the combination indices at the experimental mixture ratios only, we propose a simple parametric model for estimating the underlying interaction function. We integrate this approach into a joint model where both the parameters of the dose-response functions of the singular substances and the interaction parameters can be estimated simultaneously. As an additional benefit, this concept allows to determine optimal statistical designs for combination studies optimizing the estimation of the interaction function as a whole. From an optimal design perspective, finding the interaction parameters generally corresponds to a -optimality resp. -optimality design problem, while estimation of all underlying dose response parameters corresponds to a -optimality design problem. We show how optimal designs can be obtained in either case as well as how combination designs providing reasonable performance in regard to both criteria can be determined by putting a constraint on the efficiency in regard to one of the criteria and optimizing for the other. As all designs require prior information about model parameter values, which may be unreliable in practice, the effect of misspecifications is investigated as well.