scholarly journals Sensitivity-Based Parameter Calibration and Model Validation Under Model Error

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Na Qiu ◽  
Chanyoung Park ◽  
Yunkai Gao ◽  
Jianguang Fang ◽  
Guangyong Sun ◽  
...  
Keyword(s):  
Parameter Estimation ◽  
Calibration Method ◽  
Model Error ◽  
Model Parameters ◽  
Observation Data ◽  
Parameter Calibration ◽  
Bayesian Calibration ◽  
Modeling Errors ◽  
Model Discrepancy ◽  
Better Than

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.

Combined state-parameter estimation with the LETKF for convective-scale weather forecasting

2020 ◽  
Author(s):  
Yvonne Ruckstuhl ◽  
Tijana Janjic
Keyword(s):  
Parameter Estimation ◽  
Gaussian Noise ◽  
Roughness Length ◽  
Surface Wind ◽  
Model Error ◽  
Surface Fluxes ◽  
Model Parameters ◽  
State Variables ◽  
Augmented State ◽  
The Impact

<p>We investigate the feasibility of addressing model error by perturbing and  estimating uncertain static model parameters using the localized ensemble transform Kalman filter. In particular we use the augmented state approach, where parameters are updated by observations via their correlation with observed state variables. This online approach offers a flexible, yet consistent way to better fit model variables affected by the chosen parameters to observations, while ensuring feasible model states. We show in a nearly-operational convection-permitting configuration that the prediction of clouds and precipitation with the COSMO-DE model is improved if the two dimensional roughness length parameter is estimated with the augmented state approach. Here, the targeted model error is the roughness length itself and the surface fluxes, which influence the initiation of convection. At analysis time, Gaussian noise with a specified correlation matrix is added to the roughness length to regulate the parameter spread. In the northern part of the COSMO-DE domain, where the terrain is mostly flat and assimilated surface wind measurements are dense, estimating the roughness length led to improved forecasts of up to six hours of clouds and precipitation. In the southern part of the domain, the parameter estimation was detrimental unless the correlation length scale of the Gaussian noise that is added to the roughness length is increased. The impact of the parameter estimation was found to be larger when synoptic forcing is weak and the model output is more sensitive to the roughness length.</p>

scholarly journals Mathematical Modeling and Robustness Analysis to Unravel COVID-19 Transmission Dynamics: The Italy Case

Biology ◽  
2020 ◽  
Vol 9 (11) ◽  
pp. 394
Author(s):  
Chiara Antonini ◽  
Sara Calandrini ◽  
Fabrizio Stracci ◽  
Claudio Dario ◽  
Fortunato Bianconi
Keyword(s):  
National Level ◽  
Robustness Analysis ◽  
Calibration Method ◽  
Model Parameters ◽  
Civil Protection ◽  
Bayesian Calibration ◽  
Computational Framework ◽  
Hospitalization Rates ◽  
Intervention Measures ◽  
Umbria Region

This study started from the request of providing predictions on hospitalization and Intensive Care Unit (ICU) rates that are caused by COVID-19 for the Umbria region in Italy. To this purpose, we propose the application of a computational framework to a SEIR-type (Susceptible, Exposed, Infected, Removed) epidemiological model describing the different stages of COVID-19 infection. The model discriminates between asymptomatic and symptomatic cases and it takes into account possible intervention measures in order to reduce the probability of transmission. As case studies, we analyze not only the epidemic situation in Umbria but also in Italy, in order to capture the evolution of the pandemic at a national level. First of all, we estimate model parameters through a Bayesian calibration method, called Conditional Robust Calibration (CRC), while using the official COVID-19 data of the Italian Civil Protection. Subsequently, Conditional Robustness Analysis (CRA) on the calibrated model is carried out in order to quantify the influence of epidemiological and intervention parameters on the hospitalization rates. The proposed pipeline properly describes the COVID-19 spread during the lock-down phase. It also reveals the underestimation of new positive cases and the need of promptly isolating asymptomatic and presymptomatic cases. The results emphasize the importance of the lock-down timeliness and provide accurate predictions on the current evolution of the pandemic.

Robust Algorithms for History Matching of Imperfect Subsurface Models

SPE Journal ◽  
2020 ◽  
Vol 25 (06) ◽  
pp. 3300-3316 ◽  
Author(s):  
Muzammil H. Rammay ◽  
Ahmed H. Elsheikh ◽  
Yan Chen
Keyword(s):  
Physical Model ◽  
Covariance Matrix ◽  
History Matching ◽  
Total Error ◽  
Model Error ◽  
Error Model ◽  
Model Parameters ◽  
Model Errors ◽  
The Third ◽  
Model Discrepancy

Summary In this work, we evaluate different algorithms to account for model errors while estimating the model parameters, especially when the model discrepancy (used interchangeably with “model error”) is large. In addition, we introduce two new algorithms that are closely related to some of the published approaches under consideration. Considering all these algorithms, the first calibration approach (base case scenario) relies on Bayesian inversion using iterative ensemble smoothing with annealing schedules without any special treatment for the model error. In the second approach, the residual obtained after calibration is used to iteratively update the total error covariance combining the effects of both model errors and measurement errors. In the third approach, the principal component analysis (PCA)-based error model is used to represent the model discrepancy during history matching. This leads to a joint inverse problem in which both the model parameters and the parameters of a PCA-based error model are estimated. For the joint inversion within the Bayesian framework, prior distributions have to be defined for all the estimated parameters, and the prior distribution for the PCA-based error model parameters are generally hard to define. In this study, the prior statistics of the model discrepancy parameters are estimated using the outputs from pairs of high-fidelity and low-fidelity models generated from the prior realizations. The fourth approach is similar to the third approach; however, an additional covariance matrix of difference between a PCA-based error model and the corresponding actual realizations of prior error is added to the covariance matrix of the measurement error. The first newly introduced algorithm (fifth approach) relies on building an orthonormal basis for the misfit component of the error model, which is obtained from a difference between the PCA-based error model and the corresponding actual realizations of the prior error. The misfit component of the error model is subtracted from the data residual (difference between observations and model outputs) to eliminate the incorrect relative contribution to the prediction from the physical model and the error model. In the second newly introduced algorithm (sixth approach), we use the PCA-based error model as a physically motivated bias correction term and an iterative update of the covariance matrix of the total error during history matching. All the algorithms are evaluated using three forecasting measures, and the results show that a good parameterization of the error model is needed to obtain a good estimate of physical model parameters and to provide better predictions. In this study, the last three approaches (i.e., fourth, fifth, sixth) outperform the other methods in terms of the quality of estimated model parameters and the prediction capability of the calibrated imperfect models.

scholarly journals Parameter Estimation Based on a Local Ensemble Transform Kalman Filter Applied to El Niño–Southern Oscillation Ensemble Prediction

2021 ◽  
Vol 13 (19) ◽  
pp. 3923
Author(s):  
Yanqiu Gao ◽  
Youmin Tang ◽  
Xunshu Song ◽  
Zheqi Shen
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
Real World ◽  
El Nino ◽  
Southern Oscillation ◽  
Model Error ◽  
Model Parameters ◽  
Enso Prediction ◽  
Ensemble Transform Kalman Filter ◽  
Ensemble Transform

Parameter estimation plays an important role in reducing model error and thus is of great significance to improve the simulation and prediction capabilities of the model. However, due to filtering divergence, parameter estimation by ensemble-based filters still faces great challenges. Previous studies have shown that a covariance inflation scheme could alleviate the filtering divergence problem by increasing the signal-to-noise ratio of the state-parameter covariance. In this study, we proposed a new inflation scheme based on a local ensemble transform Kalman filter (LETKF). With the new scheme, the Zebiak–Cane (Z-C) model parameters were estimated by assimilating the sea surface temperature anomaly (SSTA) data. The effectiveness of the parameter estimation and its influence on El Niño–Southern Oscillation (ENSO) prediction were evaluated in an observation system simulation experiments (OSSE) framework and real-world scenario, respectively. With the utilization of the OSSE framework, the results showed that the model parameters were successfully estimated. Parameter estimation reduced the model error when compared with only state estimation (onlySE); however, multiple parameter estimation (MPE) further improved the ENSO prediction skill by providing better initial conditions and parameter values than the single parameter estimation (SPE). Parameter estimation could thus alleviate the spring prediction barrier (SPB) phenomenon of ENSO to a certain extent. In real-world experiments, the optimized parameters significantly improved the ENSO forecasting skill, primarily in prediction of warm events. This study provides an effective parameter estimation strategy to improve climate models and further climate predictions in the real world.

Least Bumpiness Calibration With Extrapolative Bias Correction

2018 ◽  
Author(s):  
Chanyoung Park ◽  
Nam H. Kim ◽  
Raphael T. Haftka
Keyword(s):  
Parameter Estimation ◽  
Potential Risk ◽  
Bias Correction ◽  
Model Calibration ◽  
Latin Hypercube Sampling ◽  
Calibration Method ◽  
Large Error ◽  
Parameter Estimates ◽  
Bayesian Calibration ◽  
Calibration Parameter

Bias correction is important for model calibration to obtain unbiased calibration parameter estimates and make accurate prediction. However, calibration often relies on insufficient samples, and so bias correction often mostly depends on extrapolation. For example, bias correction with twelve samples in nine-dimensional box generated by Latin Hypercube Sampling (LHS) has less than 0.1% interpolation domain in the box. Since bias correction is coupled with calibration parameter estimation, calibration with extrapolative bias correction can lead a large error in the calibrated parameters. This paper proposes an idea of calibration with minimum bumpiness correction. The bumpiness of bias correction is a good measure of assessing the potential risk of a large error in the correction. By minimizing bumpiness, the risk of extrapolation can be reduced while the accuracy of parameter estimates can be achieved. It was found that this calibration method gave more accurate results than Bayesian calibration for an analytical example. It was also found that there are common denominators between the proposed method and the Bayesian calibration with bias correction.

scholarly journals Efficient Bayesian calibration of aerodynamic wind turbine models using surrogate modeling

2021 ◽  
Author(s):  
Benjamin Sanderse ◽  
Vinit V. Dighe ◽  
Koen Boorsma ◽  
Gerard Schepers
Keyword(s):  
New Mexico ◽  
Wind Turbine ◽  
Polynomial Chaos ◽  
Global Sensitivity Analysis ◽  
Measurement Data ◽  
Model Parameters ◽  
Test Cases ◽  
Parameter Calibration ◽  
Bayesian Calibration ◽  
Polynomial Chaos Expansions

Abstract. This paper presents an efficient strategy for the Bayesian calibration of parameters of aerodynamic wind turbine models. The strategy relies on constructing a surrogate model (based on adaptive polynomial chaos expansions), which is used to perform both parameter selection using global sensitivity analysis and parameter calibration with Bayesian inference. The effectiveness of this approach is shown in two test cases: calibration of airfoil polars based on the measurements from the DanAero MW experiments, and calibration of five yaw model parameters based on measurements on the New MEXICO turbine in yawed conditions. In both cases, the calibrated models yield results much closer to the measurement data, and in addition they are equipped with an estimate of the uncertainty in the predictions.

scholarly journals Combined State-Parameter Estimation with the LETKF for Convective-Scale Weather Forecasting

2020 ◽  
Vol 148 (4) ◽  
pp. 1607-1628 ◽  
Author(s):  
Y. Ruckstuhl ◽  
T. Janjić
Keyword(s):  
Parameter Estimation ◽  
Gaussian Noise ◽  
Roughness Length ◽  
Surface Wind ◽  
Model Error ◽  
Surface Fluxes ◽  
Model Parameters ◽  
State Variables ◽  
Augmented State ◽  
The Impact

Abstract We investigate the feasibility of addressing model error by perturbing and estimating uncertain static model parameters using the localized ensemble transform Kalman filter. In particular we use the augmented state approach, where parameters are updated by observations via their correlation with observed state variables. This online approach offers a flexible, yet consistent way to better fit model variables affected by the chosen parameters to observations, while ensuring feasible model states. We show in a nearly operational convection-permitting configuration that the prediction of clouds and precipitation with the COSMO-DE model is improved if the two-dimensional roughness length parameter is estimated with the augmented state approach. Here, the targeted model error is the roughness length itself and the surface fluxes, which influence the initiation of convection. At analysis time, Gaussian noise with a specified correlation matrix is added to the roughness length to regulate the parameter spread. In the northern part of the COSMO-DE domain, where the terrain is mostly flat and assimilated surface wind measurements are dense, estimating the roughness length led to improved forecasts of up to 6 h of clouds and precipitation. In the southern part of the domain, the parameter estimation was detrimental unless the correlation length scale of the Gaussian noise that is added to the roughness length is increased. The impact of the parameter estimation was found to be larger when synoptic forcing is weak and the model output is more sensitive to the roughness length.

scholarly journals An Improved Bald Eagle Search Algorithm for Parameter Estimation of Different Photovoltaic Models

Processes ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 1127
Author(s):  
Abdelhady Ramadan ◽  
Salah Kamel ◽  
Mohamed H. Hassan ◽  
Tahir Khurshaid ◽  
Claudia Rahmann
Keyword(s):  
Parameter Estimation ◽  
Solar Cell ◽  
Silicon Solar Cell ◽  
Search Algorithm ◽  
Real Data ◽  
Clean Energy ◽  
Bald Eagle ◽  
Model Parameters ◽  
Cell Modeling ◽  
Better Than

Clean energy resources have become a worldwide concern, especially photovoltaic (PV) energy. Solar cell modeling is considered one of the most important issues in this field. In this article, an improvement for the search steps of the bald eagle search algorithm is proposed. The improved bald eagle search (IBES) was applied to estimate more accurate PV model parameters. The IBES algorithm was applied for conventional single, double, and triple PV models, in addition to modified single, double, and triple PV models. The IBES was evaluated by comparing its results with the original BES through 15 benchmark functions. For a more comprehensive analysis, two evaluation tasks were performed. In the first task, the IBES results were compared with the original BES for parameter estimation of original and modified tribe diode models. In the second task, the IBES results were compared with different recent algorithms for parameter estimation of original and modified single and double diode models. All tasks were performed using the real data for a commercial silicon solar cell (R.T.C. France). From the results, it can be concluded that the results of the modified models were more accurate than the conventional PV models, and the IBES behavior was better than the original BES and other compared algorithms.

Preliminary uncertainty analysis – a prerequisite for assessing the predictive uncertainty of hydrologic models

1996 ◽  
Vol 33 (2) ◽  
pp. 79-90 ◽  
Author(s):  
Jian Hua Lei ◽  
Wolfgang Schilling
Keyword(s):  
Uncertainty Analysis ◽  
Model Parameters ◽  
Observation Data ◽  
Calibration Data ◽  
Model Output ◽  
Predictive Uncertainty ◽  
Runoff Volume ◽  
Output Uncertainty ◽  
Sensitive Parameters ◽  
Calculated Model

Physically-based urban rainfall-runoff models are mostly applied without parameter calibration. Given some preliminary estimates of the uncertainty of the model parameters the associated model output uncertainty can be calculated. Monte-Carlo simulation followed by multi-linear regression is used for this analysis. The calculated model output uncertainty can be compared to the uncertainty estimated by comparing model output and observed data. Based on this comparison systematic or spurious errors can be detected in the observation data, the validity of the model structure can be confirmed, and the most sensitive parameters can be identified. If the calculated model output uncertainty is unacceptably large the most sensitive parameters should be calibrated to reduce the uncertainty. Observation data for which systematic and/or spurious errors have been detected should be discarded from the calibration data. This procedure is referred to as preliminary uncertainty analysis; it is illustrated with an example. The HYSTEM program is applied to predict the runoff volume from an experimental catchment with a total area of 68 ha and an impervious area of 20 ha. Based on the preliminary uncertainty analysis, for 7 of 10 events the measured runoff volume is within the calculated uncertainty range, i.e. less than or equal to the calculated model predictive uncertainty. The remaining 3 events include most likely systematic or spurious errors in the observation data (either in the rainfall or the runoff measurements). These events are then discarded from further analysis. After calibrating the model the predictive uncertainty of the model is estimated.

scholarly journals Constrained Parameter Estimation for a Mechanistic Kinetic Model of Cobalt–Hydrogen Electrochemical Competition during a Cobalt Removal Process

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 387
Author(s):  
Yiting Liang ◽  
Yuanhua Zhang ◽  
Yonggang Li
Keyword(s):  
Parameter Estimation ◽  
Kinetic Model ◽  
Model Parameters ◽  
Hydrogen Ions ◽  
Removal Process ◽  
Cobalt Removal ◽  
Estimation Scheme ◽  
Zinc Hydrometallurgy ◽  
The Impact ◽  
Parameter Estimation Scheme

A mechanistic kinetic model of cobalt–hydrogen electrochemical competition for the cobalt removal process in zinc hydrometallurgical was proposed. In addition, to overcome the parameter estimation difficulties arising from the model nonlinearities and the lack of information on the possible value ranges of parameters to be estimated, a constrained guided parameter estimation scheme was derived based on model equations and experimental data. The proposed model and the parameter estimation scheme have two advantages: (i) The model reflected for the first time the mechanism of the electrochemical competition between cobalt and hydrogen ions in the process of cobalt removal in zinc hydrometallurgy; (ii) The proposed constrained parameter estimation scheme did not depend on the information of the possible value ranges of parameters to be estimated; (iii) the constraint conditions provided in that scheme directly linked the experimental phenomenon metrics to the model parameters thereby providing deeper insights into the model parameters for model users. Numerical experiments showed that the proposed constrained parameter estimation algorithm significantly improved the estimation efficiency. Meanwhile, the proposed cobalt–hydrogen electrochemical competition model allowed for accurate simulation of the impact of hydrogen ions on cobalt removal rate as well as simulation of the trend of hydrogen ion concentration, which would be helpful for the actual cobalt removal process in zinc hydrometallurgy.

Sign in / Sign up

Export Citation Format

Share Document