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Empirical Absolute Calibration Model for Multiple Pseudo-Invariant Calibration Sites

This work extends an empirical absolute calibration model initially developed for the Libya 4 Pseudo-Invariant Calibration Site (PICS) to five additional Saharan Desert PICS (Egypt 1, Libya 1, Niger 1, Niger 2, and Sudan 1), and demonstrates the efficacy of the resulting models at predicting sensor top-of-atmosphere (TOA) reflectance. It attempts to generate absolute calibration models for these PICS that have an accuracy and precision comparable to or better than the current Libya 4 model, with the intent of providing additional opportunities for sensor calibration. In addition, this work attempts to validate the general applicability of the model to other sites. The method uses Terra Moderate Resolution Imaging Spectroradiometer (MODIS) as the reference radiometer and Earth Observing-1 (EO-1) Hyperion image data to provide a representative hyperspectral reflectance profile of the PICS. Data from a region of interest (ROI) in an “optimal region” of 3% temporal, spatial, and spectral stability within the PICS are used for developing the model. The developed models were used to simulate observations of the Landsat 7 (L7) Enhanced Thematic Mapper Plus (ETM+), Landsat 8 (L8) Operational Land Imager (OLI), Sentinel 2A (S2A) MultiSpectral Instrument (MSI) and Sentinel 2B (S2B) MultiSpectral Instrument (MSI) from their respective launch date through 2018. The models developed for the Egypt 1, Libya 1 and Sudan 1 PICS have an estimated accuracy of approximately 3% and precision of approximately 2% for the sensors used in the study, comparable to the current Libya 4 model. The models developed for the Niger 1 and Niger 2 sites are significantly less accurate with similar precision.

Raut, Bipin

Model Calibration with Markov Chain Monte Carlo Tutorial

The purpose of this tutorial is to demonstrate how to use Markov chain Monte Carlo (MCMC) to calibrate a model. By calibration, we mean the selection of model parameters (and, when relevant, structures). A common goal in model development and diagnostics is calibration, or the identification of model structures and parameters which are consistent with data. While models can be calibrated through hand-tuning parameters or minimizing simple error metrics such as root-mean-square-error (RMSE), these approaches can underrepresent the probabilistic nature of the data-generating process, as well as the potential for multiple model configurations to be consistent with the data. Probabilistic uncertainty quantification, which is the topic of this notebook, can address these concerns. This tutorial is presented as an appendix to the e-book: Addressing Uncertainty in MultiSector Dynamics Research.

Markov chain Monte Carlo

Model Calibration in Watershed Hydrology

Hydrologic models use relatively simple mathematical equations to conceptualize and aggregate the complex, spatially distributed, and highly interrelated water, energy, and vegetation processes in a watershed. A consequence of process aggregation is that the model parameters often do not represent directly measurable entities and must, therefore, be estimated using measurements of the system inputs and outputs. During this process, known as model calibration, the parameters are adjusted so that the behavior of the model approximates, as closely and consistently as possible, the observed response of the hydrologic system over some historical period of time. This Chapter reviews the current state-of-the-art of model calibration in watershed hydrology with special emphasis on our own contributions in the last few decades. We discuss the historical background that has led to current perspectives, and review different approaches for manual and automatic single- and multi-objective parameter estimation. In particular, we highlight the recent developments in the calibration of distributed hydrologic models using parameter dimensionality reduction sampling, parameter regularization and parallel computing.

Yilmaz, Koray K.

A Comparison of Two Balance Calibration Model Building Methods

Simulated strain-gage balance calibration data is used to compare the accuracy of two balance calibration model building methods for different noise environments and calibration experiment designs. The first building method obtains a math model for the analysis of balance calibration data after applying a candidate math model search algorithm to the calibration data set. The second building method uses stepwise regression analysis in order to construct a model for the analysis. Four balance calibration data sets were simulated in order to compare the accuracy of the two math model building methods. The simulated data sets were prepared using the traditional One Factor At a Time (OFAT) technique and the Modern Design of Experiments (MDOE) approach. Random and systematic errors were introduced in the simulated calibration data sets in order to study their influence on the math model building methods. Residuals of the fitted calibration responses and other statistical metrics were compared in order to evaluate the calibration models developed with different combinations of noise environment, experiment design, and model building method. Overall, predicted math models and residuals of both math model building methods show very good agreement. Significant differences in model quality were attributable to noise environment, experiment design, and their interaction. Generally, the addition of systematic error significantly degraded the quality of calibration models developed from OFAT data by either method, but MDOE experiment designs were more robust with respect to the introduction of a systematic component of the unexplained variance.

DeLoach, Richard

Reduced-dimension Bayesian optimization for model calibration of transient vapor compression cycles

Development and calibration of first-principles dynamic models of vapor compression cycles (VCCs) is of critical importance for applications that include control design and fault detection and diagnostics. Nevertheless, the inherent complexity of models that are represented by large systems of differential–algebraic equations leads to significant challenges for model calibration processes that utilize classical gradient-based methods. Bayesian optimization (BO) is a sample-efficient and gradient-free approach using a probabilistic surrogate model and optimal search over a feasible parameter space. Despite the benefits of BO in reducing computational costs, challenges remain in dealing with a high-dimensional calibration task resulting from a large set of parameters that have significant impacts on system behavior and need to be calibrated simultaneously. This paper presents a reduced-dimension BO framework for calibrating transient VCCs models where the calibration space is projected to a low-dimensional subspace for accelerating convergence of the solution algorithm and consequently reducing the number of transient simulations. The proposed approach was demonstrated via two case studies associated with different VCC applications where 10 parameters were calibrated in each case using laboratory measurements. The reduced-dimension BO framework only required 1 / 8 th of the iterations associated with a standard BO method that deals with high-dimensional calibration parameters for converged solutions and yielded comparable accuracy. Furthermore, both calibrated models revealed significant accuracy improvements compared to uncalibrated models.

Ma, Jiacheng

Elastic Bayesian Model Calibration

Functional data are ubiquitous in scientific modeling. For instance, quantities of interest are modeled as functions of time, space, energy, density, etc. Uncertainty quantification methods for computer models with functional response have resulted in tools for emulation, sensitivity analysis, and calibration that are widely used. However, many of these tools do not perform well when the computer model’s parameters control both the amplitude variation of the functional output and its alignment (or phase variation). This paper introduces a framework for Bayesian model calibration when the model responses are misaligned functional data. The approach generates two types of data out of the misaligned functional responses: (1) aligned functions so that the amplitude variation is isolated and (2) warping functions that isolate the phase variation. These two types of data are created for the computer simulation data (both of which may be emulated) and the experimental data. The calibration approach uses both types so that it seeks to match both the amplitude and phase of the experimental data. The framework is careful to respect constraints that arise, especially when modeling phase variation, and is framed in a way that it can be done with readily available calibration software. In conclusion, we demonstrate the techniques on two simulated data examples and on two dynamic material science problems: a strength model calibration using flyer plate experiments and an equation of state model calibration using experiments performed on the Sandia National Laboratories’ Z-machine.

97 MATHEMATICS AND COMPUTING

Model Calibration for Cancer Risk Projections According to Uncertain Data

This paper presents forward and inverse formulations for the calibration of computational models according to uncertain data. Uncertainty in the data might be caused by a poor metrology system, measurement noise, missing or uncontrollable input variables, or by the inability to directly measure the inputs and/or outputs of interest. The forward approach performs the calibration in the space of the model’s output thereby requiring repeated model simulations. Conversely, the inverse approach leverages an ensemble of solutions to an inverse problem in order to perform the calibration in the space of the model’s parameters. As such, the computational demands of the inverse approach are considerably lower. These strategies are applied to the calibration of a radiation model that in-forms cancer risk projections for future deep space missions.

uncertainty quantification

Leveraging Pre-storm Soil Moisture Estimates for Enhanced Land Surface Model Calibration in Ungauged Hydrologic Basins

Despite long-standing efforts, hydrologists still lack robust tools for calibrating land surface model (LSM) streamflow estimates within ungauged basins. Using surface soil moisture estimates from the Soil Moisture Active Passive Level 4 Soil Moisture (L4_SM) product, precipitation observations, and streamflow gauge measurements for 617 medium-scale (200-10,000 km2) basins in the contiguous United States, we measure the temporal (Spearman) rank correlation between antecedent (i.e., pre-storm) surface soil moisture (ASM) and the storm-scale runoff coefficient (RC; the fraction of storm-scale precipitation accumulation converted into streamflow). In humid and semi-humid basins, this rank correlation is shown to be sufficiently strong to allow for the substitution of storm-scale RC observations (available only in basins that are both lightly regulated and gauged) with high-quality ASM values (available quasi-globally from L4_SM) in streamflow calibration procedures. Using this principle, we define a new, basin-wise LSM streamflow calibration approach based on L4_SM alone and successfully apply it to identify LSM configurations that produce a high rank correlation with observed RC. However, since the approach cannot detect RC bias, it is less successful in identifying LSM configurations with low mean-absolute error. Plain Text Summary Accurately forecasting the fraction of rainfall that runs off into streams, as opposed to infiltrates into the soil, is critical for flash-flood prediction, water-resource monitoring, and tracking the transport of nutrients from agricultural fields into local waterways. Such forecasting is typically performed by hydrologic models that attempt to represent the physical processes responsible for surface runoff generation. However, to provide accurate streamflow forecasts, these models typically need to be calibrated against actual streamflow observations. This is problematic given the relatively poor, and declining, global availability of stream gauges. This paper presents a novel model calibration strategy that uses soil moisture from remote sensing and numerical modeling in place of streamflow observations during calibration. This transition has significant practical advantages because, unlike streamflow observations, the soil moisture data are continuously available across space. Our results demonstrate that this new approach can significantly improve hydrologic models within humid and semi-humid basins lacking sufficient ground-based instrumentation for traditional streamflow calibration.

hydrologic models

Advancements in Constitutive Model Calibration: Leveraging the Power of Full‐Field DIC Measurements and In Situ Load Path Selection for Reliable Parameter Inference

Accurate material characterization and model calibration are essential for computationally supported high-consequence engineering decisions. Historically, characterization and calibration methods (1) use simplified test specimen geometries and global data, (2) cannot guarantee that sufficient characterization data are collected for a specific model of interest, (3) use deterministic methods that provide best-fit parameter values with no uncertainty quantification, and (4) are sequential, inflexible, and time-consuming. This work brings together several recent advancements into an improved workflow called interlaced characterization and calibration (ICC) that advances the state-of-the-art in constitutive model calibration. The ICC paradigm (1) employs tools to efficiently use full-field data to calibrate high-fidelity material models, (2) aligns the data needed with the data collected by adopting an optimal experimental design protocol, (3) quantifies parameter uncertainty through Bayesian inference and (4) incorporates these advancements into a quasi real-time feedback loop. The ICC framework is demonstrated here on the calibration of a material model using simulated full-field data for an aluminium cruciform specimen being deformed biaxially. The cruciform is actively driven through the myopically preferred load path using Bayesian optimal experimental design, which selects load steps that yield the maximum expected information gain (EIG). Principal component analysis (PCA) is performed on the model predictions of full-field displacements, and fast surrogate models are built to approximate the input-output relationships of the expensive finite element model. Furthermore, the tools developed and demonstrated here show that high-fidelity constitutive models can be efficiently and reliably calibrated with quantified uncertainty, thus supporting credible decision-making and potentially increasing the agility of solid mechanics modelling by enabling utilization of computational simulations at earlier stages of the design cycle.

Bayesian optimal experimental design

Finite Element Model Calibration Approach for Ares I-X

Ares I-X is a pathfinder vehicle concept under development by NASA to demonstrate a new class of launch vehicles. Although this vehicle is essentially a shell of what the Ares I vehicle will be, efforts are underway to model and calibrate the analytical models before its maiden flight. Work reported in this document will summarize the model calibration approach used including uncertainty quantification of vehicle responses and the use of nonconventional boundary conditions during component testing. Since finite element modeling is the primary modeling tool, the calibration process uses these models, often developed by different groups, to assess model deficiencies and to update parameters to reconcile test with predictions. Data for two major component tests and the flight vehicle are presented along with the calibration results. For calibration, sensitivity analysis is conducted using Analysis of Variance (ANOVA). To reduce the computational burden associated with ANOVA calculations, response surface models are used in lieu of computationally intensive finite element solutions. From the sensitivity studies, parameter importance is assessed as a function of frequency. In addition, the work presents an approach to evaluate the probability that a parameter set exists to reconcile test with analysis. Comparisons of pre-test predictions of frequency response uncertainty bounds with measured data, results from the variance-based sensitivity analysis, and results from component test models with calibrated boundary stiffness models are all presented.

Horta, Lucas G.

Finite Element Model Calibration Approach for Area I-X

Ares I-X is a pathfinder vehicle concept under development by NASA to demonstrate a new class of launch vehicles. Although this vehicle is essentially a shell of what the Ares I vehicle will be, efforts are underway to model and calibrate the analytical models before its maiden flight. Work reported in this document will summarize the model calibration approach used including uncertainty quantification of vehicle responses and the use of non-conventional boundary conditions during component testing. Since finite element modeling is the primary modeling tool, the calibration process uses these models, often developed by different groups, to assess model deficiencies and to update parameters to reconcile test with predictions. Data for two major component tests and the flight vehicle are presented along with the calibration results. For calibration, sensitivity analysis is conducted using Analysis of Variance (ANOVA). To reduce the computational burden associated with ANOVA calculations, response surface models are used in lieu of computationally intensive finite element solutions. From the sensitivity studies, parameter importance is assessed as a function of frequency. In addition, the work presents an approach to evaluate the probability that a parameter set exists to reconcile test with analysis. Comparisons of pretest predictions of frequency response uncertainty bounds with measured data, results from the variance-based sensitivity analysis, and results from component test models with calibrated boundary stiffness models are all presented.

Horta, Lucas G.

Calibrating Historical IR Sensors Using GEO, and AVHRR Infrared Tropical Mean Calibration Models

Long-term, remote-sensing-based climate data records (CDRs) are highly dependent on having consistent, wellcalibrated satellite instrument measurements of the Earth's radiant energy. Therefore, by making historical satellite calibrations consistent with those of today's imagers, the Earth-observing community can benefit from a CDR that spans a minimum of 30 years. Most operational meteorological satellites rely on an onboard blackbody and space looks to provide on-orbit IR calibration, but neither target is traceable to absolute standards. The IR channels can also be affected by ice on the detector window, angle dependency of the scan mirror emissivity, stray-light, and detector-to-detector striping. Being able to quantify and correct such degradations would mean IR data from any satellite imager could contribute to a CDR. Recent efforts have focused on utilizing well-calibrated modern hyper-spectral sensors to intercalibrate concurrent operational IR imagers to a single reference. In order to consistently calibrate both historical and current IR imagers to the same reference, however, another strategy is needed. Large, well-characterized tropical-domain Earth targets have the potential of providing an Earth-view reference accuracy of within 0.5 K. To that effort, NASA Langley is developing an IR tropical mean calibration model in order to calibrate historical Advanced Very High Resolution Radiometer (AVHRR) instruments. Using Meteosat-9 (Met-9) as a reference, empirical models are built based on spatially/temporally binned Met-9 and AVHRR tropical IR brightness temperatures. By demonstrating the stability of the Met-9 tropical models, NOAA-18 AVHRR can be calibrated to Met-9 by matching the AVHRR monthly histogram averages with the Met-9 model. This method is validated with ray-matched AVHRR and Met-9 biasdifference time series. Establishing the validity of this empirical model will allow for the calibration of historical AVHRR sensors to within 0.5 K, and thereby establish a climate-quality IR data record.

Scarino, Benjamin

2002 VCMPO Model Calibration and Home-Based Travel Survey

The 2001-2002 Model Calibration and Home-Based Travel Survey was a study conducted in Volusia County, Florida. One of the major purposes of the survey project was to collect information to allow for a better understanding of the travel habits and patterns of residents within Volusia County. The project was jointly funded by the Florida Department of Transportation, Volusia County, and the Volusia County MPO. Demographic and trip data were collected for 2,727 households from February 20, 2002, to February 28, 2002. Respondents were asked to record their travel and activities for a 48-hour period. Detailed information regarding their trips, including mode of transportation, trip purpose, departure and arrival times, and number of passengers, were gathered from 13,408 trips.

1Hz data

On the Use of Optimization Techniques for Turbulence Model Calibration

This article discusses the use of numerical optimization procedures to aid in the calibration of turbulence model coefficients. Such methods would increase the rigor and repeatability of the calibration procedure by requiring clearly defined and objective optimization metrics, and could be used to identify unique combinations of coefficient values for specific flow problems. The approach is applied to the re-calibration of an explicit algebraic Reynolds stress model for the incompressible planar mixing layer using the Nelder-Mead simplex algorithm and a micro-genetic algorithm with minimally imposed constraints. Three composite fitness functions, each based upon the error in the mixing layer growth rate and the normal and shear components of the Reynolds stresses, are investigated. The results demonstrate a significant improvement in the target objectives through the adjustment of three pressure-strain coefficients. Adjustments of additional coefficients provide little further benefit. Issues regarding the effectiveness of the fitness functions and the efficiency of the optimization algorithms are also discussed.

Yoder, Dennis A.

The tropospheric calibration model for Mariner Mars 1971

The effects of the troposphere on arrival time, range, and range rate measurement of radio signals propagating from spacecraft are examined. A tropospheric calibration model which takes into account seasonal variations, various elevations, and apparent location changes was developed. A comparison was made of the effects before and after calibration. Without calibration, a 16-m change in the distance off the spin axis, is induced for a 10-deg minimum elevation symmetrical pass. Even after calibration with the old model, the error in spin axis is still greater than 1 m. Calibration results and estimated uncertainties of the model are given in tabular form. Test results also show that the model met the required accuracy for the Mariner Mars 1971 mission.

C. C. Chao

A direct-adjoint approach for material point model calibration with application to plasticity

Here, this paper proposes a new approach for the calibration of material parameters in local elastoplastic constitutive models. The calibration is posed as a constrained optimization problem, where the constitutive model evolution equations for a single material point serve as constraints. The objective function quantifies the mismatch between the stress predicted by the model and corresponding experimental measurements. To improve calibration efficiency, a novel direct-adjoint approach is presented to compute the Hessian of the objective function, which enables the use of second-order optimization algorithms. Automatic differentiation is used for gradient and Hessian computations. Two numerical examples are employed to validate the Hessian matrices and to demonstrate that the Newton–Raphson algorithm consistently outperforms gradient-based algorithms such as L-BFGS-B.

36 MATERIALS SCIENCE

Model Calibration Efforts for the International Space Station's Solar Array Mast

The International Space Station (ISS) relies on sixteen solar-voltaic blankets to provide electrical power to the station. Each pair of blankets is supported by a deployable boom called the Folding Articulated Square Truss Mast (FAST Mast). At certain ISS attitudes, the solar arrays can be positioned in such a way that shadowing of either one or three longerons causes an unexpected asymmetric thermal loading that if unchecked can exceed the operational stability limits of the mast. Work in this paper documents part of an independent NASA Engineering and Safety Center effort to assess the existing operational limits. Because of the complexity of the system, the problem is being worked using a building-block progression from components (longerons), to units (single or multiple bays), to assembly (full mast). The paper presents results from efforts to calibrate the longeron components. The work includes experimental testing of two types of longerons (straight and tapered), development of Finite Element (FE) models, development of parameter uncertainty models, and the establishment of a calibration and validation process to demonstrate adequacy of the models. Models in the context of this paper refer to both FE model and probabilistic parameter models. Results from model calibration of the straight longerons show that the model is capable of predicting the mean load, axial strain, and bending strain. For validation, parameter values obtained from calibration of straight longerons are used to validate experimental results for the tapered longerons.

Elliott, Kenny B.