Model Discrepancy Research Articles

Regulation control of an underactuated mechanical system with discontinuous friction and backlash

AbstractIn this work, the problem of position regulation control is addressed for a 2DOF underactuated mechanical system with friction and backlash. For this purpose, a method combining sliding mode and H∞control is developed. We prove that the application of the method to the nonlinear model considered results in an asymptotically stable equilibria set. Moreover, it is possible to achieve a sufficiently small and bounded steady-state position error even in the presence of disturbances by employing the proposed technique. That is, the developed controller is able to account not only for unmatched external perturbations and model discrepancies of the test rig considered, but also for matched bounded perturbations. The control methodology is presented from both the theoretical and experimental angles to demonstrate the good performance of the proposed controller.

Lepton mass effects and angular observables in Λb→Λ(→pπ)ℓ+ℓ−

The flavor changing rare decay $B\to K^{*}(\to K\pi)\ell^+\ell^-$ is one of the most studied modes due to its sensitivity to physics beyond the standard model and several discrepancies have come to light among the plethora of observables that are measured. In this paper we revisit the analogous baryonic decay mode $\Lambda_{b}\rightarrow \Lambda (\to p\pi) \ell^{+}\ell^{-}$ and we present a complete set of ten angular observables that can be measured using this decay mode. Our calculations are done retaining the finite lepton mass so that the signal of lepton non-universality observed in $B\to K^{*} \ell^+\ell^-$ can be corroborated by the corresponding baryonic decay mode. We show that due to the parity violating nature of the subsequent $\Lambda\to p\pi$ decay there exist at least one angular asymmetry that is non-vanishing in the large recoil limit unlike the case in $B\to K^{*}\ell^+\ell^-$ decay mode, making it particularly sensitive to new physics that violates lepton flavor universality.

Constitutive model error and uncertainty quantification

AbstractThis paper proposes a novel Bayesian strategy for high‐dimensional inverse problems in the context of elastostatics. Apart from parametric uncertainties, model inadequacies and, particularly, constitutive model errors, are also addressed. This is especially important in biomedical settings when the inferred material properties will be used to make decisions/diagnoses. Traditional approaches use an additional regression model (e.g., Gaussian process), added to the model output or within a submodel to account, for an underlying model error. This can violate physical constraints and becomes impractical in high dimensions.In this work we unfold conservation and constitutive laws to estimate model discrepancies. In addition, efficient Bayesian strategies are employed. In elastography, the accurate identification of the unknown mechanical properties of a tissue as well as the associated uncertainty, can greatly assist noninvasive, medical diagnosis. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Sensitivity-Based Parameter Calibration and Model Validation Under Model Error

In calibrating model parameters, it is important to include the model discrepancy term in order to capture missing physics in simulation, which can result from numerical, measurement, and modeling errors. Ignoring the discrepancy may lead to biased calibration parameters and predictions, even with an increasing number of observations. In this paper, a simple yet efficient calibration method is proposed based on sensitivity information when the simulation model has a model error and/or numerical error but only a small number of observations are available. The sensitivity-based calibration method captures the trend of observation data by matching the slope of simulation predictions and observations at different designs and then utilizing a constant value to compensate for the model discrepancy. The sensitivity-based calibration is compared with the conventional least squares calibration method and Bayesian calibration method in terms of parameter estimation and model prediction accuracies. A cantilever beam example, as well as a honeycomb tube crush example, is used to illustrate the calibration process of these three methods. It turned out that the sensitivity-based method has a similar performance with the Bayesian calibration method and performs much better than the conventional method in parameter estimation and prediction accuracy.

Aerosol-type retrieval and uncertainty quantification from OMI data

Abstract. We discuss uncertainty quantification for aerosol-type selection in satellite-based atmospheric aerosol retrieval. The retrieval procedure uses precalculated aerosol microphysical models stored in look-up tables (LUTs) and top-of-atmosphere (TOA) spectral reflectance measurements to solve the aerosol characteristics. The forward model approximations cause systematic differences between the modelled and observed reflectance. Acknowledging this model discrepancy as a source of uncertainty allows us to produce more realistic uncertainty estimates and assists the selection of the most appropriate LUTs for each individual retrieval.This paper focuses on the aerosol microphysical model selection and characterisation of uncertainty in the retrieved aerosol type and aerosol optical depth (AOD). The concept of model evidence is used as a tool for model comparison. The method is based on Bayesian inference approach, in which all uncertainties are described as a posterior probability distribution. When there is no single best-matching aerosol microphysical model, we use a statistical technique based on Bayesian model averaging to combine AOD posterior probability densities of the best-fitting models to obtain an averaged AOD estimate. We also determine the shared evidence of the best-matching models of a certain main aerosol type in order to quantify how plausible it is that it represents the underlying atmospheric aerosol conditions.The developed method is applied to Ozone Monitoring Instrument (OMI) measurements using a multiwavelength approach for retrieving the aerosol type and AOD estimate with uncertainty quantification for cloud-free over-land pixels. Several larger pixel set areas were studied in order to investigate the robustness of the developed method. We evaluated the retrieved AOD by comparison with ground-based measurements at example sites. We found that the uncertainty of AOD expressed by posterior probability distribution reflects the difficulty in model selection. The posterior probability distribution can provide a comprehensive characterisation of the uncertainty in this kind of problem for aerosol-type selection. As a result, the proposed method can account for the model error and also include the model selection uncertainty in the total uncertainty budget.

An Evaluation of Ion Channel Screening Uncertainty vs. Action Potential Model Discrepancy As Sources of Error in Predictions of QT Prolongation

An Evaluation of Ion Channel Screening Uncertainty vs. Action Potential Model Discrepancy As Sources of Error in Predictions of QT Prolongation

Implications of allometric model selection for county-level biomass mapping

BackgroundCarbon accounting in forests remains a large area of uncertainty in the global carbon cycle. Forest aboveground biomass is therefore an attribute of great interest for the forest management community, but the accuracy of aboveground biomass maps depends on the accuracy of the underlying field estimates used to calibrate models. These field estimates depend on the application of allometric models, which often have unknown and unreported uncertainties outside of the size class or environment in which they were developed.ResultsHere, we test three popular allometric approaches to field biomass estimation, and explore the implications of allometric model selection for county-level biomass mapping in Sonoma County, California. We test three allometric models: Jenkins et al. (For Sci 49(1): 12–35, 2003), Chojnacky et al. (Forestry 87(1): 129–151, 2014) and the US Forest Service’s Component Ratio Method (CRM). We found that Jenkins and Chojnacky models perform comparably, but that at both a field plot level and a total county level there was a ~ 20% difference between these estimates and the CRM estimates. Further, we show that discrepancies are greater in high biomass areas with high canopy covers and relatively moderate heights (25–45 m). The CRM models, although on average ~ 20% lower than Jenkins and Chojnacky, produce higher estimates in the tallest forests samples (> 60 m), while Jenkins generally produces higher estimates of biomass in forests < 50 m tall. Discrepancies do not continually increase with increasing forest height, suggesting that inclusion of height in allometric models is not primarily driving discrepancies. Models developed using all three allometric models underestimate high biomass and overestimate low biomass, as expected with random forest biomass modeling. However, these deviations were generally larger using the Jenkins and Chojnacky allometries, suggesting that the CRM approach may be more appropriate for biomass mapping with lidar.ConclusionsThese results confirm that allometric model selection considerably impacts biomass maps and estimates, and that allometric model errors remain poorly understood. Our findings that allometric model discrepancies are not explained by lidar heights suggests that allometric model form does not drive these discrepancies. A better understanding of the sources of allometric model errors, particularly in high biomass systems, is essential for improved forest biomass mapping.

Refining mass formulas for astrophysical applications: A Bayesian neural network approach

Exotic nuclei, particularly those near the driplines, are at the core of one of the fundamental questions driving nuclear structure and astrophysics today: what are the limits of nuclear binding? Exotic nuclei play a critical role in both informing theoretical models as well as in our understanding of the origin of the heavy elements. Our purpose is to refine existing mass models through the training of an artificial neural network that will mitigate the large model discrepancies far away from stability. The basic paradigm of our two-pronged approach is an existing mass model that captures as much as possible of the underlying physics followed by the implementation of a Bayesian Neural Network (BNN) refinement to account for the missing physics. Bayesian inference is employed to determine the parameters of the neural network so that model predictions may be accompanied by theoretical uncertainties. Despite the undeniable quality of the mass models adopted in this work, we observe a significant improvement (of about 40%) after the BNN refinement is implemented. Indeed, in the specific case of the Duflo-Zuker mass formula, we find that the rms deviation relative to experiment is reduced from rms =0.503MeV to rms=0.286 MeV. These newly refined mass tables are used to map the neutron drip lines (or rather "drip bands") and to study a few critical r-process nuclei. The BNN approach is highly successful in refining the predictions of existing mass models. In particular, the large discrepancy displayed by the original "bare" models in regions where experimental data is unavailable is considerably quenched after the BNN refinement. This lends credence to our approach and has motivated us to publish refined mass tables that we trust will be helpful for future astrophysical applications.

Upscaling Uncertainty with Dynamic Discrepancy for a Multi-Scale Carbon Capture System

ABSTRACTUncertainties from model parameters and model discrepancy from small-scale models impact the accuracy and reliability of predictions of large-scale systems. Inadequate representation of these uncertainties may result in inaccurate and overconfident predictions during scale-up to larger systems. Hence, multiscale modeling efforts must accurately quantify the effect of the propagation of uncertainties during upscaling. Using a Bayesian approach, we calibrate a small-scale solid sorbent model to thermogravimetric (TGA) data on a functional profile using chemistry-based priors. Crucial to this effort is the representation of model discrepancy, which uses a Bayesian smoothing splines (BSS-ANOVA) framework. Our uncertainty quantification (UQ) approach could be considered intrusive as it includes the discrepancy function within the chemical rate expressions; resulting in a set of stochastic differential equations. Such an approach allows for easily propagating uncertainty by propagating the joint model parameter and discrepancy posterior into the larger-scale system of rate expressions. The broad UQ framework presented here could be applicable to virtually all areas of science where multiscale modeling is used. Supplementary materials for this article are available online.

Issues with the measurement of informal care in social surveys: evidence from the English Longitudinal Study of Ageing

ABSTRACTInformal care plays a significant role in the care system for older people in the United Kingdom, and this is projected to increase considerably in the next three decades as the population ages. Understanding these trends requires a good quality measurement of informal care. In this study, we compare care-givers’ responses to different informal care questions from the English Longitudinal Study of Ageing (ELSA) to investigate the influence of question design on the self-reporting of informal care. We also analyse spousal care dyads in order to model discrepancies in the reporting of care provision between spouses to provide an insight into the reliability of informal care measurements. We find that the most common measures used are likely to be under-estimating both the scale and scope of informal care, and we recommend careful consideration of the content of informal care survey questions in order to operationalise the measures of informal care activities.

Propagation of Input Uncertainty in Presence of Model-Form Uncertainty: A Multifidelity Approach for Computational Fluid Dynamics Applications

Proper quantification and propagation of uncertainties in computational simulations are of critical importance. This issue is especially challenging for computational fluid dynamics (CFD) applications. A particular obstacle for uncertainty quantifications in CFD problems is the large model discrepancies associated with the CFD models used for uncertainty propagation. Neglecting or improperly representing the model discrepancies leads to inaccurate and distorted uncertainty distribution for the quantities of interest (QoI). High-fidelity models, being accurate yet expensive, can accommodate only a small ensemble of simulations and thus lead to large interpolation errors and/or sampling errors; low-fidelity models can propagate a large ensemble, but can introduce large modeling errors. In this work, we propose a multimodel strategy to account for the influences of model discrepancies in uncertainty propagation and to reduce their impact on the predictions. Specifically, we take advantage of CFD models of multiple fidelities to estimate the model discrepancies associated with the lower-fidelity model in the parameter space. A Gaussian process (GP) is adopted to construct the model discrepancy function, and a Bayesian approach is used to infer the discrepancies and corresponding uncertainties in the regions of the parameter space where the high-fidelity simulations are not performed. Several examples of relevance to CFD applications are performed to demonstrate the merits of the proposed strategy. Simulation results suggest that, by combining low- and high-fidelity models, the proposed approach produces better results than what either model can achieve individually.

Combined iterative learning and delta-operator adaptive linear quadratic Gaussian control of a commercial rapid thermal processing system

Rapid thermal processing (RTP) units are used for various semiconductor fabrication steps mainly due to the short processing time, which results in a low thermal budget and improved product quality. In this study, we propose a comprehensive control system for the RTP unit by combining a linear quadratic Gaussian (LQG) controller, a constrained iterative learning controller (ILC), and a model parameter estimator. The control system is developed to resolve the issues caused by a short sampling time, which is required to meet the refractory control objectives of the modern RTP system (e.g., rapid ramping and a high degree of temperature uniformity). LQG control is selected because most required computations are conducted offline prior to each run and only minor computations are conducted in real time. The LQG control is constructed in a Smith predictor configuration so that a delayed model can be easily incorporated. The LQG control algorithm is modified from the standard formulation to include a quadratic penalty term for input deviation from the average value, to restrain the inputs from violating their constraints in real-time operation. The control algorithm and process model are developed in delta form so that the effect of the truncation error on the model accuracy can be alleviated at a high sampling rate. The constrained ILC updates the feedforward signal of the LQG controller in a batch-wise manner to further increase the temperature uniformity and to ensure that the inputs satisfy their constraints. To overcome model discrepancy from an actual system (patterned wafer), a small number of tunable parameters that can modify the major characteristics of the process model are incorporated into the identified state-space model (bare wafer) and are updated by a model parameter estimator. The performance of the proposed control system is validated in a numerical process, which is precisely constructed through identification experiments in a commercial 12-inch RTP unit.

Adaptive Uncertainty Propagation for Coupled Multidisciplinary Systems

This paper presents a novel uncertainty propagation approach for multidisciplinary systems with feedback couplings, model discrepancy, and parametric uncertainty. The proposed method incorporates aspects of Gibbs sampling, importance resampling, and density estimation to ensure that, under mild assumptions, the current method is provably convergent in distribution. The method uses the samples available from previously simulating the disciplines by applying sequential importance resampling. The absence or lack of samples in each discipline is addressed by introducing an adaptive greedy sample increment process to improve the efficiency of uncertainty analysis with minimum possible computational cost. A key feature of the approach is that disciplinary models are all synthesized independently based on their available data, and it does not require any full coupled system-level evaluations. The proposed approach is illustrated on the propagation of uncertainty for an aerodynamics–structures system and is compared to a system-level Monte Carlo uncertainty analysis approach.

INTER-COMPARISON OF RECENT TIDE MODELS FOR THE PERSIAN GULF AND OMAN SEA

Using several series of field measurements data along Iranian coastline of the Persian Gulf and Gulf of Oman, eight different tide models have been evaluated in this study. By comparing the results in the frequency domain, it was found that the model discrepancies arise in shallow waters, having maximum error in the shallowest part of the Persian Gulf, where Pohl station is located. On the other hand, maximum error of tide models is limited to 10 cm in deeper part of the Persian Gulf, indicating that different tide models result in close outcome in deeper waters. Considering the results in the time domain, it was found that FES model, which includes more shallow water constituents, results in better tidal level predictions. FES also presents the best tidal current predictions in the area of the interest of this study.

Sensitivity analysis and Bayesian calibration for testing robustness of the BASGRA model in different environments

Proper parameterisation and quantification of model uncertainty are two essential tasks in improvement and assessment of model performance. Bayesian calibration is a method that combines both tasks by quantifying probability distributions for model parameters and outputs. However, the method is rarely applied to complex models because of its high computational demand when used with high-dimensional parameter spaces. We therefore combined Bayesian calibration with sensitivity analysis, using the screening method by Morris (1991), in order to reduce model complexity by fixing parameters to which model output was only weakly sensitive to a nominal value. Further, the robustness of the model with respect to reduction in the number of free parameters were examined according to model discrepancy and output uncertainty. The process-based grassland model BASGRA was examined in the present study on two sites in Norway and in Germany, for two grass species (Phleum pratense and Arrhenatherum elatius). According to this study, a reduction of free model parameters from 66 to 45 was possible. The sensitivity analysis showed that the parameters to be fixed were consistent across sites (which differed in climate and soil conditions), while model calibration had to be performed separately for each combination of site and species. The output uncertainty decreased slightly, but still covered the field observations of aboveground biomass. Considering the training data, the mean square error for both the 66 and the 45 parameter model was dominated by errors in timing (phase shift), whereas no general pattern was found in errors when using the validation data. Stronger model reduction should be avoided, as the error term increased and output uncertainty was underestimated.

Identification and causes of metabonomic difference between orthotopic and subcutaneous xenograft of pancreatic cancer.

Pancreatic ductal adenocarcinoma (PDAC) is one of the most lethal tumors. However, the methodological differences between orthotopic and subcutaneous xenograft (OX and SX) models will cause confusion in understanding its pathological mechanism and clinical relevance. In this study, SX and OX models were established by implanting Panc-1 and BxPC-3 cell strains under skin and on the pancreas of mice, respectively. The tumor tissue and serum samples were collected for1H NMR spectroscopy followed by univariate and multivariate statistical analyses. As results, no obvious metabonomic difference was demonstrated in serum between the two models, however, the model- and cell strain-specific metabonomic differences were observed in tumor tissues. According to the KEGG analysis, ABC transporters, glycerophospholipid metabolism, purine metabolism and central carbon metabolism were identified to be the most significant components involved in metabonomic differences. Considering the methodological discrepancy in SX and OX models, such differences should be contributed to tumor microenvironment. In general, SX are not equivalent to OX models at molecular level. Subcutaneous transplantation displayed its inherent limitations though it offered a simple, inexpensive, reproducible and quantifiable advantage. And orthotopic transplantation may be favorable to simulate PDAC in patients due to its similar pathogenesis to human pancreatic cancer.

Kinerja Program Studi Administrasi Pendidikan Fakultas Ilmu Pendidikan Universitas Negeri Jakarta (Ditinjau dari Pelayanan dalam Bidang Kurikulum, Sistem Pembelajaran, dan Suasana Akademik)

Research conducted at the Administration of Education Study Program Facultyof Education, State University of Jakarta. This reasearch aimed to describe theperformance of the study program in providing good educational services for students aslearners through curriculum applied by the program of study which includes theperformance of courses in the curriculum development system is supported by learningand academic atmosphere. This study is an evaluative method deskripstif conducted tosee the performance of Administration of Education Study Program Faculty of Education,State University of Jakarta using a qualitative and quantitative approach. Evaluationmodel used is the model Discrepancy Evaluation Model (DEM). The data obtained byresearchers is through observation, interviews, and documentation. Key informantinterviews were conducted to the Chairman of Study Program UNJ AP FIP, and issupported by a supporter informant consisting of lecturers, TU Staff, and Student StudyProgram UNJ AP FIP.The reasearch concluded that 1) the performance component of courses onaspects of curriculum development shows the categories very good, 2) the performancecomponent of courses there are aspects of the implementation of learning systems, fromfour (4) aspects of the implementation of the learning system there are two componentsindicate the category of very good: execution learning process, efforts to improve thelearning system. Components of the implementation of the guiding thesis showed goodcategory. While the implementation of the components of academic guidance indicatesless category. 3) the performance component of study program there is the aspect ofincreasing academic atmosphere, showing very good category. Based on the acquisitionof these three components, it can be said the performance of the study program ofEducational Administration Faculty of Education at the Jakarta State UniversityCurricula Aspects, Learning Systems and academic atmosphere showed very goodcategory.

Machine-Learning-Augmented Predictive Modeling of Turbulent Separated Flows over Airfoils

A modeling paradigm is developed to augment predictive models of turbulence by effectively using limited data generated from physical experiments. The key components of the current approach involve inverse modeling to infer the spatial distribution of model discrepancies and machine learning to reconstruct discrepancy information from a large number of inverse problems into corrective model forms. The methodology is applied to turbulent flows over airfoils involving flow separation. Model augmentations are developed for the Spalart–Allmaras model using adjoint-based full-field inference on experimentally measured lift coefficient data. When these model forms are reconstructed using neural networks and embedded within a standard solver, it is shown that much improved predictions in lift can be obtained for geometries and flow conditions that were not used to train the model. The neural-network-augmented Spalart–Allmaras model also predicts surface pressures extremely well. Portability of this approach is demonstrated by confirming that predictive improvements are preserved when the augmentation is embedded in a different commercial, finite element solver. The broader vision is that, by incorporating data that can reveal the form of the innate model discrepancy, the applicability of data-driven turbulence models can be extended to more general flows.

NAO and its relationship with the Northern Hemisphere mean surface temperature in CMIP5 simulations

AbstractThe North Atlantic Oscillation (NAO) is one of the most prominent teleconnection patterns in the Northern Hemisphere and has recently been found to be both an internal source and useful predictor of the multidecadal variability of the Northern Hemisphere mean surface temperature (NHT). In this study, we examine how well the variability of the NAO and NHT are reproduced in historical simulations generated by the 40 models that constitute Phase 5 of the Coupled Model Intercomparison Project (CMIP5). All of the models are able to capture the basic characteristics of the interannual NAO pattern reasonably well, whereas the simulated decadal NAO patterns show less consistency with the observations. The NAO fluctuations over multidecadal time scales are underestimated by almost all models. Regarding the NHT multidecadal variability, the models generally represent the externally forced variations well but tend to underestimate the internal NHT. With respect to the performance of the models in reproducing the NAO‐NHT relationship, 14 models capture the observed decadal lead of the NAO, and model discrepancies in the representation of this linkage are derived mainly from their different interpretation of the underlying physical processes associated with the Atlantic Multidecadal Oscillation (AMO) and the Atlantic meridional overturning circulation (AMOC). This study suggests that one way to improve the simulation of the multidecadal variability of the internal NHT lies in better simulation of the multidecadal variability of the NAO and its delayed effect on the NHT variability via slow ocean processes.

Identification of dynamical systems with structured uncertainty

In this paper, we consider the problem of parameter identification for models defined by dynamical systems with structured uncertainty. This type of problem often occurs in science and engineering and we show how parameter estimation can be improved by taking advantage of the specific structure of the model form. We distinguish between model identification and model calibration and discuss approaches to deal with model discrepancy when the systems are described by classes of parameterized models where the uncertainties have a specified structure. The results are applicable to problems where, in the process of modelling a complex system, one ignores ‘small’ parameters to obtain simplified models and when infinite-dimensional systems are approximated to obtain finite-dimensional models. We show for these common sources of model discrepancies, hierarchical modelling can be employed to aid in the development of prior knowledge about the model form caused by uncertain or ignored parameters. We focus on a special class of inverse problems arising from model calibration and parameter estimation and illustrate how one can use information about the structure of the dynamical system to help deal with model discrepancy. Examples from the life sciences and engineering design are given to illustrate the ideas.