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Journal articles on the topic 'Parameter uncertainty'

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Author: Grafiati

Published: 4 June 2021

Last updated: 31 January 2023

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1

Kim, Eung Seok. "Analysis of Runoff According to Application of SWMM-LID Element Technology (II): Parameter Uncertainty Analysis." Journal of the Korean Society of Hazard Mitigation 20, no. 6 (December 31, 2020): 445–50. http://dx.doi.org/10.9798/kosham.2020.20.6.445.

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This study quantitatively analyzed the degree of uncertainty associated with runoff based on the sensitivity analysis of runoff parameters using Low Impact Development (LID) element technology of study (I). Uncertainty was analyzed for parameter uncertainty, uncertainty of runoff, and uncertainty about the degree of parameter and runoff. Parameter uncertainty indices showed lower uncertainty indices as a whole and uncertainty indices of peak runoff were higher than that of total runoff in runoff uncertainty. The reason for this is that the LID element technology itself is intended to store low-frequency small-scale rainfall, so that the uncertainty index of peak rainfall seems to be highly uncertain. As a result of the analysis of uncertainty degree associated with runoff, it was found that the uncertainty of storage depth of bio retention cell and rain garden was low, while the heaviness parameters of rain barrel had the highest uncertainty index. In future experiments and research, it is necessary to modify the parameter range suitable for Korea, which will be helpful for urban development, reduction of nonpoint source pollution, and designing of low frequency rainfall storage facilities.

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2

Højberg, A. L., and J. C. Refsgaard. "Model uncertainty – parameter uncertainty versus conceptual models." Water Science and Technology 52, no. 6 (September 1, 2005): 177–86. http://dx.doi.org/10.2166/wst.2005.0166.

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Uncertainties in model structures have been recognised often to be the main source of uncertainty in predictive model simulations. Despite this knowledge, uncertainty studies are traditionally limited to a single deterministic model and the uncertainty addressed by a parameter uncertainty study. The extent to which a parameter uncertainty study may encompass model structure errors in a groundwater model is studied in a case study. Three groundwater models were constructed on the basis of three different hydrogeological interpretations. Each of the models was calibrated inversely against groundwater heads and streamflows. A parameter uncertainty analysis was carried out for each of the three conceptual models by Monte Carlo simulations. A comparison of the predictive uncertainties for the three conceptual models showed large differences between the uncertainty intervals. Most discrepancies were observed for data types not used in the model calibration. Thus uncertainties in the conceptual models become of increasing importance when predictive simulations consider data types that are extrapolates from the data types used for calibration.

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3

Chen, Si, Guoqi Xie, Renfa Li, and Keqin Li. "Uncertainty Theory Based Partitioning for Cyber-Physical Systems with Uncertain Reliability Analysis." ACM Transactions on Design Automation of Electronic Systems 27, no. 3 (May 31, 2022): 1–19. http://dx.doi.org/10.1145/3490177.

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Reasonable partitioning is a critical issue for cyber-physical system (CPS) design. Traditional CPS partitioning methods run in a determined context and depend on the parameter pre-estimations, but they ignore the uncertainty of parameters and hardly consider reliability. The state-of-the-art work proposed an uncertainty theory based CPS partitioning method, which includes parameter uncertainty and reliability analysis, but it only considers linear uncertainty distributions for variables and ignores the uncertainty of reliability. In this paper, we propose an uncertainty theory based CPS partitioning method with uncertain reliability analysis. We convert the uncertain objective and constraint into determined forms; such conversion methods can be applied to all forms of uncertain variables, not just for linear. By applying uncertain reliability analysis in the uncertainty model, we for the first time include the uncertainty of reliability into the CPS partitioning, where the reliability enhancement algorithm is proposed. We study the performance of the reliability obtained through uncertain reliability analysis, and experimental results show that the system reliability with uncertainty does not change significantly with the growth of task module numbers.

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4

Weise, K. "Uncertainty of Parameter Estimation." IFAC Proceedings Volumes 18, no. 5 (July 1985): 1717–22. http://dx.doi.org/10.1016/s1474-6670(17)60816-4.

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5

Paulter, N. G., and D. R. Larson. "Pulse parameter uncertainty analysis." Metrologia 39, no. 2 (April 2002): 143–55. http://dx.doi.org/10.1088/0026-1394/39/2/4.

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6

Wakeland, Wayne, and Jack Homer. "Addressing Parameter Uncertainty in a Health Policy Simulation Model Using Monte Carlo Sensitivity Methods." Systems 10, no. 6 (November 18, 2022): 225. http://dx.doi.org/10.3390/systems10060225.

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We present a practical guide and step-by-step flowchart for establishing uncertainty in-tervals for key model outcomes in a simulation model in the face of uncertain parameters. The process start with Powell optimization to find a set of uncertain parameters (the optimum param-eter set or OPS) that minimize the model fitness error relative to historical data. Optimization also help in refinement of parameter uncertainty ranges. Next, traditional Monte Carlo (TMC) ran-domization or Markov Chain Monte Carlo (MCMC) is used to create a sample of parameter sets that fit the reference behavior data nearly as well as the OPS. Under the TMC method, the entire pa-rameter space is explored broadly with a large number of runs, and the results are sorted for se-lection of qualifying parameter sets (QPS) to ensure good fit and parameter distributions that are centrally located within the uncertainty ranges. In addition, the QPS outputs are graphed as sen-sitivity graphs or box-and-whisker plots for comparison with the historical data. Finally, alternative policies and scenarios are run against the OPS and all QPS, and uncertainty intervals are found for projected model outcomes. We illustrate the full parameter uncertainty approach with a (previ-ously published) system dynamics model of the U.S. opioid epidemic, and demonstrate how it can enrich policy modeling results.

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7

Bai, Jie, Shuai Liu, and Wei Wang. "Study on Identification Method for Parameter Uncertainty Model of Aero Engine." International Journal of Aerospace Engineering 2019 (December 2, 2019): 1–9. http://dx.doi.org/10.1155/2019/6015270.

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The linear model of an aero engine is effective in a small range of the neighborhood of equilibrium points. According to this problem, the identification method for the parameter uncertain linear model of the aero engine was proposed. The identification problem is solved by calculating nonlinear programming. Considering the parameter uncertainty of the model is the critical point of this research during the optimization process. A parameter uncertain model of an aero engine can be obtained, which has large use range. This method is used for DGEN380 aero engine. The two parameters, VDD and VE, are defined for describing error range. Compared with experimental data, the uncertain model of DGEN 380 can simulate the real state of DGEN380 within 1% error range when ΔPLA<22%. Compared with another conventional method of identification (recursive least squares), the parameter uncertain model, established by the method of this research, has a broad application area through parameter uncertainty of the model.

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8

Mousavi, S. Jamshid, K. C. Abbaspour, B. Kamali, M. Amini, and H. Yang. "Uncertainty-based automatic calibration of HEC-HMS model using sequential uncertainty fitting approach." Journal of Hydroinformatics 14, no. 2 (May 10, 2011): 286–309. http://dx.doi.org/10.2166/hydro.2011.071.

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This study presents the application of an uncertainty-based technique for automatic calibration of the well-known Hydrologic Engineering Center-Hydrologic Modelling System (HEC-HMS) model. Sequential uncertainty fitting (SUFI2) approach has been used in calibration of the HEC-HMS model built for Tamar basin located in north of Iran. The basin was divided into seven sub-basins and three routing reaches with 24 parameters to be estimated. From the four events, three were used for calibration and one for verification. Each event was initially calibrated separately. As there was no unique parameter set identified, all events were then calibrated jointly. Based on the scenarios of separately and jointly calibrated events, different candidate parameter sets were inputted to the model verification stage where recalibration of initial abstraction parameters commenced. Some of the candidate parameter sets with no physically meaningful parameter values were withdrawn after recalibration. Then new ranges of parameters were identified based on minimum and maximum values of the remaining parameter sets. The new parameter ranges were used in an uncertainty analysis using SUFI2 technique resulting in much narrower parameter intervals that can simulate both verification and calibration events satisfactorily in a probabilistic sense. Results show that the SUFI2 technique linked to HEC-HMS as a simulation–optimization model can provide a basis for performing uncertainty-based automatic calibration of event-based hydrologic models.

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9

Pernot, Pascal. "The parameter uncertainty inflation fallacy." Journal of Chemical Physics 147, no. 10 (September 14, 2017): 104102. http://dx.doi.org/10.1063/1.4994654.

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10

Gerrard, R., and A. Tsanakas. "Failure Probability Under Parameter Uncertainty." Risk Analysis 31, no. 5 (December 22, 2010): 727–44. http://dx.doi.org/10.1111/j.1539-6924.2010.01549.x.

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11

Monoyios, M. "Optimal hedging and parameter uncertainty." IMA Journal of Management Mathematics 18, no. 4 (April 26, 2007): 331–51. http://dx.doi.org/10.1093/imaman/dpm022.

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12

Hansen, Bruce E. "Interval forecasts and parameter uncertainty." Journal of Econometrics 135, no. 1-2 (November 2006): 377–98. http://dx.doi.org/10.1016/j.jeconom.2005.07.030.

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13

Al-Najjar, Nabil I., and Eran Shmaya. "Recursive utility and parameter uncertainty." Journal of Economic Theory 181 (May 2019): 274–88. http://dx.doi.org/10.1016/j.jet.2019.02.005.

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14

Siegert, Stefan, Philip G. Sansom, and Robin M. Williams. "Parameter uncertainty in forecast recalibration." Quarterly Journal of the Royal Meteorological Society 142, no. 696 (February 9, 2016): 1213–21. http://dx.doi.org/10.1002/qj.2716.

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15

Lee, L. A., K. S. Carslaw, K. Pringle, G. W. Mann, and D. V. Spracklen. "Emulation of a complex global aerosol model to quantify sensitivity to uncertain parameters." Atmospheric Chemistry and Physics Discussions 11, no. 7 (July 19, 2011): 20433–85. http://dx.doi.org/10.5194/acpd-11-20433-2011.

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Abstract. Sensitivity analysis of atmospheric models is necessary to identify the processes that lead to uncertainty in model predictions, to help understand model diversity, and to prioritise research. Assessing the effect of parameter uncertainty in complex models is challenging and often limited by CPU constraints. Here we present a cost-effective application of variance-based sensitivity analysis to quantify the sensitivity of a 3-D global aerosol model to uncertain parameters. A Gaussian process emulator is used to estimate the model output across multi-dimensional parameter space using information from a small number of model runs at points chosen using a Latin hypercube space-filling design. Gaussian process emulation is a Bayesian approach that uses information from the model runs along with some prior assumptions about the model behaviour to predict model output everywhere in the uncertainty space. We use the Gaussian process emulator to calculate the percentage of expected output variance explained by uncertainty in global aerosol model parameters and their interactions. To demonstrate the technique, we show examples of cloud condensation nuclei (CCN) sensitivity to 8 model parameters in polluted and remote marine environments as a function of altitude. In the polluted environment 95 % of the variance of CCN concentration is described by uncertainty in the 8 parameters (excluding their interaction effects) and is dominated by the uncertainty in the sulphur emissions, which explains 80 % of the variance. However, in the remote region parameter interaction effects become important, accounting for up to 40 % of the total variance. Some parameters are shown to have a negligible individual effect but a substantial interaction effect. Such sensitivities would not be detected in the commonly used single parameter perturbation experiments, which would therefore underpredict total uncertainty. Gaussian process emulation is shown to be an efficient and useful technique for quantifying parameter sensitivity in complex global atmospheric model.

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16

Lee, L. A., K. S. Carslaw, K. J. Pringle, G. W. Mann, and D. V. Spracklen. "Emulation of a complex global aerosol model to quantify sensitivity to uncertain parameters." Atmospheric Chemistry and Physics 11, no. 23 (December 8, 2011): 12253–73. http://dx.doi.org/10.5194/acp-11-12253-2011.

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Abstract. Sensitivity analysis of atmospheric models is necessary to identify the processes that lead to uncertainty in model predictions, to help understand model diversity through comparison of driving processes, and to prioritise research. Assessing the effect of parameter uncertainty in complex models is challenging and often limited by CPU constraints. Here we present a cost-effective application of variance-based sensitivity analysis to quantify the sensitivity of a 3-D global aerosol model to uncertain parameters. A Gaussian process emulator is used to estimate the model output across multi-dimensional parameter space, using information from a small number of model runs at points chosen using a Latin hypercube space-filling design. Gaussian process emulation is a Bayesian approach that uses information from the model runs along with some prior assumptions about the model behaviour to predict model output everywhere in the uncertainty space. We use the Gaussian process emulator to calculate the percentage of expected output variance explained by uncertainty in global aerosol model parameters and their interactions. To demonstrate the technique, we show examples of cloud condensation nuclei (CCN) sensitivity to 8 model parameters in polluted and remote marine environments as a function of altitude. In the polluted environment 95 % of the variance of CCN concentration is described by uncertainty in the 8 parameters (excluding their interaction effects) and is dominated by the uncertainty in the sulphur emissions, which explains 80 % of the variance. However, in the remote region parameter interaction effects become important, accounting for up to 40 % of the total variance. Some parameters are shown to have a negligible individual effect but a substantial interaction effect. Such sensitivities would not be detected in the commonly used single parameter perturbation experiments, which would therefore underpredict total uncertainty. Gaussian process emulation is shown to be an efficient and useful technique for quantifying parameter sensitivity in complex global atmospheric models.

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17

Hagen, David R., Jacob K. White, and Bruce Tidor. "Convergence in parameters and predictions using computational experimental design." Interface Focus 3, no. 4 (August 6, 2013): 20130008. http://dx.doi.org/10.1098/rsfs.2013.0008.

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Typically, biological models fitted to experimental data suffer from significant parameter uncertainty, which can lead to inaccurate or uncertain predictions. One school of thought holds that accurate estimation of the true parameters of a biological system is inherently problematic. Recent work, however, suggests that optimal experimental design techniques can select sets of experiments whose members probe complementary aspects of a biochemical network that together can account for its full behaviour. Here, we implemented an experimental design approach for selecting sets of experiments that constrain parameter uncertainty. We demonstrated with a model of the epidermal growth factor–nerve growth factor pathway that, after synthetically performing a handful of optimal experiments, the uncertainty in all 48 parameters converged below 10 per cent. Furthermore, the fitted parameters converged to their true values with a small error consistent with the residual uncertainty. When untested experimental conditions were simulated with the fitted models, the predicted species concentrations converged to their true values with errors that were consistent with the residual uncertainty. This paper suggests that accurate parameter estimation is achievable with complementary experiments specifically designed for the task, and that the resulting parametrized models are capable of accurate predictions.

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18

Cooke, Roger M. "Parameter fitting for uncertain models: modelling uncertainty in small models." Reliability Engineering & System Safety 44, no. 1 (January 1994): 89–102. http://dx.doi.org/10.1016/0951-8320(94)90110-4.

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19

Tang, Hesheng, Xueyuan Guo, Liyu Xie, and Songtao Xue. "Experimental Validation of Optimal Parameter and Uncertainty Estimation for Structural Systems Using a Shuffled Complex Evolution Metropolis Algorithm." Applied Sciences 9, no. 22 (November 18, 2019): 4959. http://dx.doi.org/10.3390/app9224959.

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The uncertainty in parameter estimation arises from structural systems’ input and output measured errors and from structural model errors. An experimental verification of the shuffled complex evolution metropolis algorithm (SCEM-UA) for identifying the optimal parameters of structural systems and estimating their uncertainty is presented. First, the estimation framework is theoretically developed. The SCEM-UA algorithm is employed to search through feasible parameters’ space and to infer the posterior distribution of the parameters automatically. The resulting posterior parameter distribution then provides the most likely estimation of parameter sets that produces the best model performance. The algorithm is subsequently validated through both numerical simulation and shaking table experiment for estimating the parameters of structural systems considering the uncertainty of available information. Finally, the proposed algorithm is extended to identify the uncertain physical parameters of a nonlinear structural system with a particle mass tuned damper (PTMD). The results demonstrate that the proposed algorithm can effectively estimate parameters with uncertainty for nonlinear structural systems, and it has a stronger anti-noise capability. Notably, the SCEM-UA method not only shows better global optimization capability compared with other heuristic optimization methods, but it also has the ability to simultaneously estimate the uncertainties associated with the posterior distributions of the structural parameters within a single optimization run.

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20

Christensen, H. M., I. M. Moroz, and T. N. Palmer. "Stochastic and Perturbed Parameter Representations of Model Uncertainty in Convection Parameterization*." Journal of the Atmospheric Sciences 72, no. 6 (May 27, 2015): 2525–44. http://dx.doi.org/10.1175/jas-d-14-0250.1.

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Abstract It is now acknowledged that representing model uncertainty in atmospheric simulators is essential for the production of reliable probabilistic forecasts, and a number of different techniques have been proposed for this purpose. This paper presents new perturbed parameter schemes for use in the European Centre for Medium-Range Weather Forecasts (ECMWF) convection scheme. Two types of scheme are developed and implemented. Both schemes represent the joint uncertainty in four of the parameters in the convection parameterization scheme, which was estimated using the Ensemble Prediction and Parameter Estimation System (EPPES). The first scheme developed is a fixed perturbed parameter scheme, where the values of uncertain parameters are varied between ensemble members, but held constant over the duration of the forecast. The second is a stochastically varying perturbed parameter scheme. The performance of these schemes was compared to the ECMWF operational stochastic scheme, stochastically perturbed parameterization tendencies (SPPT), and to a model that does not represent uncertainty in convection. The skill of probabilistic forecasts made using the different models was evaluated. While the perturbed parameter schemes improve on the stochastic parameterization in some regards, the SPPT scheme outperforms the perturbed parameter approaches when considering forecast variables that are particularly sensitive to convection. Overall, SPPT schemes are the most skillful representations of model uncertainty owing to convection parameterization.

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21

Inoue, Kazuya, Ippei Masaki, and Tsutomu Tanaka. "Monitoring Network Design for Detection of Groundwater Contamination under Parameter Uncertainty." Journal of Rainwater Catchment Systems 10, no. 2 (2005): 11–18. http://dx.doi.org/10.7132/jrcsa.kj00004364656.

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22

Roy, Bijan Kumar. "Optimum Performance of Bridge Isolation System under Parameter Uncertainty." International Journal of Geotechnical Earthquake Engineering 8, no. 2 (July 2017): 82–101. http://dx.doi.org/10.4018/ijgee.2017070105.

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This article deals with the study of optimum performance of isolated bridge systems under stochastic earthquake load considering uncertain system parameters. The conditional stochastic response quantities are obtained in random vibration framework using the state space formulation. Subsequently, with the aid of matrix perturbation theory using first order Taylor series expansion of dynamic response function and its interval extension, the vibration control problem is transformed to appropriate deterministic optimization problems. This requires two separate objective functions correspond to a lower and upper bound optimum solutions. A lead rubber bearing system for isolating a bridge deck from a pier is considered for numerical study to elucidate the optimum performance of isolated bridge deck system. Then a numerical study is performed to observe the effect of parameter uncertainty on the optimization of the isolator parameters and the response reduction efficiency. It is seen that neglecting the effect of system parameter uncertainty may overestimate the system performance.

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23

Lee, L. A., K. S. Carslaw, K. J. Pringle, and G. W. Mann. "Mapping the uncertainty in global CCN using emulation." Atmospheric Chemistry and Physics 12, no. 20 (October 25, 2012): 9739–51. http://dx.doi.org/10.5194/acp-12-9739-2012.

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Abstract. In the last two IPCC assessments aerosol radiative forcings have been given the largest uncertainty range of all forcing agents assessed. This forcing range is really a diversity of simulated forcings in different models. An essential step towards reducing model uncertainty is to quantify and attribute the sources of uncertainty at the process level. Here, we use statistical emulation techniques to quantify uncertainty in simulated concentrations of July-mean cloud condensation nuclei (CCN) from a complex global aerosol microphysics model. CCN was chosen because it is the aerosol property that controls cloud drop concentrations, and therefore the aerosol indirect radiative forcing effect. We use Gaussian process emulation to perform a full variance-based sensitivity analysis and quantify, for each model grid box, the uncertainty in simulated CCN that results from 8 uncertain model parameters. We produce global maps of absolute and relative CCN sensitivities to the 8 model parameter ranges and derive probability density functions for simulated CCN. The approach also allows us to include the uncertainty from interactions between these parameters, which cannot be quantified in traditional one-at-a-time sensitivity tests. The key findings from our analysis are that model CCN in polluted regions and the Southern Ocean are mostly only sensitive to uncertainties in emissions parameters but in all other regions CCN uncertainty is driven almost exclusively by uncertainties in parameters associated with model processes. For example, in marine regions between 30° S and 30° N model CCN uncertainty is driven mainly by parameters associated with cloud-processing of Aitken-sized particles whereas in polar regions uncertainties in scavenging parameters dominate. In these two regions a single parameter dominates but in other regions up to 50% of the variance can be due to interaction effects between different parameters. Our analysis provides direct quantification of the reduction in variance that would result if a parameter could be specified precisely. When extended to all process parameters the approach presented here will therefore provide a clear global picture of how improved knowledge of aerosol processes would translate into reduced model uncertainty.

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24

Emery, A. F., and T. D. Fadale. "Design of Experiments Using Uncertainty Information." Journal of Heat Transfer 118, no. 3 (August 1, 1996): 532–38. http://dx.doi.org/10.1115/1.2822664.

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The process of parameter estimation and the estimated parameters are affected not only by measurement noise, which is present during any experiment, but also by uncertainties in the parameters of the model used to describe the system. This paper describes a method to optimize the design of an experiment to deduce the maximum information during the inverse problem of parameter estimation in the presence of uncertainties in the model parameters. It is shown that accounting for these uncertainties affects the optimal locations of the sensors.

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25

Cai, Longyan, Hong S. He, Yu Liang, Zhiwei Wu, and Chao Huang. "Analysis of the uncertainty of fuel model parameters in wildland fire modelling of a boreal forest in north-east China." International Journal of Wildland Fire 28, no. 3 (2019): 205. http://dx.doi.org/10.1071/wf18083.

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Fire propagation is inevitably affected by fuel-model parameters during wildfire simulations and the uncertainty of the fuel-model parameters makes forecasting accurate fire behaviour very difficult. In this study, three different methods (Morris screening, first-order analysis and the Monte Carlo method) were used to analyse the uncertainty of fuel-model parameters with FARSITE model. The results of the uncertainty analysis showed that only a few fuel-model parameters markedly influenced the uncertainty of the model outputs, and many of the fuel-model parameters had little or no effect. The fire-spread rate is the driving force behind the uncertainty of other fire behaviours. Thus, the highly uncertain fuel-model parameters associated with spread rate should be used cautiously in wildfire simulations. Monte Carlo results indicated that the relationship between model input and output was non-linear and neglecting fuel-model parameter uncertainty of the model would magnify fire behaviours. Additionally, fuel-model parameters have high input uncertainty. Therefore, fuel-model parameters must be calibrated against actual fires. The highly uncertain fuel-model parameters with high spatial-temporal variability consisted of fuel-bed depth, live-shrub loading and 1-h time-lag loading are preferentially chosen as parameters to calibrate several wildfires.

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26

Ray, L. R. "Robust Linear-Optimal Control Laws for Active Suspension Systems." Journal of Dynamic Systems, Measurement, and Control 114, no. 4 (December 1, 1992): 592–98. http://dx.doi.org/10.1115/1.2897729.

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The stability robustness of linear-optimal control laws for quarter-car active suspension systems is evaluated using stochastic robustness analysis. Simultaneous parameters variations and neglected actuator and sensor dynamics are considered for LQ active suspension systems and for a single-measurement LQG system to determine the effects of uncertainty on system stability. The results indicate that neglected actuator and sensor dynamics have a small effect on stability robustness, while parameter uncertainty, particularly that of the “sprung mass” is of great concern. The effectiveness of Loop Transfer Recovery on active suspension systems with both parameter uncertainty and higher-order uncertainty is discerned. The analysis shows that when Loop Transfer Recovery is applied arbitrarily to uncertain systems, both estimator performance and system robustness can decrease. Nevertheless, it is concluded that the impact of the robustness recovery method is determined by stochastic stability robustness analysis, and the recovery design parameter that provides sufficient robustness with minimal performance degradation is readily identified. The effect of LQ design parameters on robustness also is considered. The paper presents robustness analysis and synthesis methods for a quarter-car model that can be applied to higher-order active suspension systems.

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27

Conrad, Y., and N. Fohrer. "Application of the Bayesian calibration methodology for the parameter estimation in CoupModel." Advances in Geosciences 21 (August 10, 2009): 13–24. http://dx.doi.org/10.5194/adgeo-21-13-2009.

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Abstract. This study provides results for the optimization strategy of highly parameterized models, especially with a high number of unknown input parameters and joint problems in terms of sufficient parameter space. Consequently, the uncertainty in model parameterization and measurements must be considered when highly variable nitrogen losses, e.g. N leaching, are to be predicted. The Bayesian calibration methodology was used to investigate the parameter uncertainty of the process-based CoupModel. Bayesian methods link prior probability distributions of input parameters to likelihood estimates of the simulation results by comparison with measured values. The uncertainty in the updated posterior parameters can be used to conduct an uncertainty analysis of the model output. A number of 24 model variables were optimized during 20 000 simulations to find the "optimum" value for each parameter. The likelihood was computed by comparing simulation results with observed values of 23 output variables including soil water contents, soil temperatures, groundwater level, soil mineral nitrogen, nitrate concentrations below the root zone, denitrification and harvested carbon from grassland plots in Northern Germany for the period 1997–2002. The posterior parameter space was sampled with the Markov Chain Monte Carlo approach to obtain plot-specific posterior parameter distributions for each system. Posterior distributions of the parameters narrowed down in the accepted runs, thus uncertainty decreased. Results from the single-plot optimization showed a plausible reproduction of soil temperatures, soil water contents and water tensions in different soil depths for both systems. The model performed better for these abiotic system properties compared to the results for harvested carbon and soil mineral nitrogen dynamics. The high variability in modeled nitrogen leaching showed that the soil nitrogen conditions are highly uncertain associated with low modeling efficiencies. Simulated nitrate leaching was compared to more general, site-specific estimations, indicating a higher leaching during the seepage periods for both simulated grassland systems.

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28

Liu, Chang, and Duane A. McVay. "Continuous Reservoir-Simulation-Model Updating and Forecasting Improves Uncertainty Quantification." SPE Reservoir Evaluation & Engineering 13, no. 04 (August 12, 2010): 626–37. http://dx.doi.org/10.2118/119197-pa.

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Summary Most reservoir-simulation studies are conducted in a static context—at a single point in time using a fixed set of historical data for history matching. Time and budget constraints usually result in significant reduction in the number of uncertain parameters and incomplete exploration of the parameter space, which results in underestimation of forecast uncertainty and less-than-optimal decision making. Markov Chain Monte Carlo (MCMC) methods have been used in static studies for rigorous exploration of the parameter space for quantification of forecast uncertainty, but these methods suffer from long burn-in times and many required runs for chain stabilization. In this paper, we apply the MCMC in a real-time reservoirmodeling application. The system operates in a continuous process of data acquisition, model calibration, forecasting, and uncertainty quantification. The system was validated on the PUNQ (production forecasting with uncertainty quantification) synthetic reservoir in a simulated multiyear continuous-modeling scenario, and it yielded probabilistic forecasts that narrowed with time. Once the continuous MCMC simulation process has been established sufficiently, the continuous approach usually allows generation of a reasonable probabilistic forecast at a particular point in time with many fewer models than the traditional application of the MCMC method in a one-time, static simulation study starting at the same time. Operating continuously over the many years of typical reservoir life, many more realizations can be run than with traditional approaches. This allows more-thorough investigation of the parameter space and more-complete quantification of forecast uncertainty. More importantly, the approach provides a mechanism for, and can thus encourage, calibration of uncertainty estimates over time. Greater investigation of the uncertain parameter space and calibration of uncertainty estimates by using a continuous modeling process should improve the reliability of probabilistic forecasts significantly.

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29

Lee, L. A., K. S. Carslaw, K. J. Pringle, and G. W. Mann. "Mapping the uncertainty in global CCN using emulation." Atmospheric Chemistry and Physics Discussions 12, no. 6 (June 6, 2012): 14089–114. http://dx.doi.org/10.5194/acpd-12-14089-2012.

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Abstract. In the last two IPCC assessment reports aerosol radiative forcings have been given the largest uncertainty range of all forcing agents assessed. This forcing range is really a diversity of simulated forcings in different models and an essential step towards reducing it is to quantify and attribute sources of model uncertainty at the process level. Here, we use statistical emulation techniques to quantify uncertainty in simulated concentrations of July-mean cloud condensation nuclei (CCN) from a complex global aerosol microphysics model. Specifically, we use Gaussian process emulation to give a full variance-based sensitivity analysis and quantify, for each model grid box, the uncertainty in simulated CCN that results from 8 uncertain model parameters. We produce global maps of absolute and relative CCN sensitivities to the 8 model parameter ranges and derive probability density functions for simulated CCN. The approach also allows us to include the uncertainty from interactions between these parameters, which cannot be quantified in traditional one-at-a-time sensitivity tests. The key findings from our analysis are that model CCN in polluted regions and the Southern Ocean are mostly only sensitive to uncertainties in emissions parameters but in all other regions CCN uncertainty is driven almost exclusively by uncertainties in parameters for model processes. For example, in marine regions between 30° S and 30° N model CCN uncertainty is driven mainly by parameters associated with cloud-processing of Aitken-sized particles whereas in polar regions uncertainties in scavenging parameters dominate. In these two regions a single parameter dominates but in other regions up to 50% of the variance can be due to interaction effects between different parameters. Our analysis provides direct quantification of the reduction in variance that would result if a parameter could be specified precisely. When extended to all process parameters the approach presented here will therefore provide a clear global picture of how improved knowledge of aerosol processes would translate into reduced model uncertainty.

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30

Shin and Kim. "Analysis of the Effect of Uncertainty in Rainfall-Runoff Models on Simulation Results Using a Simple Uncertainty-Screening Method." Water 11, no. 7 (June 30, 2019): 1361. http://dx.doi.org/10.3390/w11071361.

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Various uncertainty analysis methods have been used in various studies to analyze the uncertainty of rainfall-runoff models; however, these methods are difficult to apply immediately as they require a long learning time. In this study, we propose a simple uncertainty-screening method that allows modelers to investigate relatively easily the uncertainty of rainfall-runoff models. The 100 best parameter values of three rainfall-runoff models were extracted using the efficient sampler DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm, and the distribution of the parameter values was investigated. Additionally, the ranges of the values of a model performance evaluation statistic and indicators of hydrologic alteration corresponding to the 100 parameter values for the calibration and validation periods was analyzed. The results showed that the Sacramento model, which has the largest number of parameters, had uncertainties in parameters, and the uncertainty of one parameter influenced all other parameters. Furthermore, the uncertainty in the prediction results of the Sacramento model was larger than those of other models. The IHACRES model had uncertainty in one parameter related to the slow flow simulation. On the other hand, the GR4J model had the lowest uncertainty compared to the other two models. The uncertainty-screening method presented in this study can be easily used when the modelers select rainfall-runoff models with lower uncertainty.

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31

Iskra, Igor, and Ronald Droste. "Parameter Uncertainty of a Watershed Model." Canadian Water Resources Journal 33, no. 1 (January 2008): 5–22. http://dx.doi.org/10.4296/cwrj3301005.

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32

Tao, Ye, Francesco Ferranti, and Michel S. Nakhla. "Uncertainty Quantification Using Parameter Space Partitioning." IEEE Transactions on Microwave Theory and Techniques 69, no. 4 (April 2021): 2110–19. http://dx.doi.org/10.1109/tmtt.2021.3059668.

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Coles, Jeffrey L., Uri Loewenstein, and Jose Suay. "On Equilibrium Pricing under Parameter Uncertainty." Journal of Financial and Quantitative Analysis 30, no. 3 (September 1995): 347. http://dx.doi.org/10.2307/2331345.

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34

Geromel, J. C. "Optimal linear filtering under parameter uncertainty." IEEE Transactions on Signal Processing 47, no. 1 (1999): 168–75. http://dx.doi.org/10.1109/78.738249.

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Nazin, Sergey A., and Boris T. Polyak*. "Interval parameter estimation under model uncertainty." Mathematical and Computer Modelling of Dynamical Systems 11, no. 2 (June 2005): 225–37. http://dx.doi.org/10.1080/138950500069243.

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Stenarson, J., and K. Yhland. "Uncertainty Propagation Through Network Parameter Conversions." IEEE Transactions on Instrumentation and Measurement 58, no. 4 (April 2009): 1152–57. http://dx.doi.org/10.1109/tim.2008.2008578.

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37

Bontemps, Christian. "Moment-Based Tests under Parameter Uncertainty." Review of Economics and Statistics 101, no. 1 (March 2019): 146–59. http://dx.doi.org/10.1162/rest_a_00745.

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38

Ng, Szu Hui, and Stephen E. Chick. "Reducing parameter uncertainty for stochastic systems." ACM Transactions on Modeling and Computer Simulation 16, no. 1 (January 2006): 26–51. http://dx.doi.org/10.1145/1122012.1122014.

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39

Bignozzi, Valeria, and Andreas Tsanakas. "Parameter Uncertainty and Residual Estimation Risk." Journal of Risk and Insurance 83, no. 4 (March 16, 2015): 949–78. http://dx.doi.org/10.1111/jori.12075.

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40

Booth, Laurence. "Discounting expected values with parameter uncertainty." Journal of Corporate Finance 9, no. 5 (November 2003): 505–19. http://dx.doi.org/10.1016/s0929-1199(02)00020-2.

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41

Rogers, L. C. G. "The relaxed investor and parameter uncertainty." Finance and Stochastics 5, no. 2 (April 2001): 131–54. http://dx.doi.org/10.1007/pl00013532.

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42

Koop, Gary. "Parameter uncertainty and impulse response analysis." Journal of Econometrics 72, no. 1-2 (May 1996): 135–49. http://dx.doi.org/10.1016/0304-4076(94)01717-4.

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43

Kan, Raymond, and Guofu Zhou. "Optimal Portfolio Choice with Parameter Uncertainty." Journal of Financial and Quantitative Analysis 42, no. 3 (September 2007): 621–56. http://dx.doi.org/10.1017/s0022109000004129.

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AbstractIn this paper, we analytically derive the expected loss function associated with using sample means and the covariance matrix of returns to estimate the optimal portfolio. Our analytical results show that the standard plug-in approach that replaces the population parameters by their sample estimates can lead to very poor out-of-sample performance. We further show that with parameter uncertainty, holding the sample tangency portfolio and the riskless asset is never optimal. An investor can benefit by holding some other risky portfolios that help reduce the estimation risk. In particular, we show that a portfolio that optimally combines the riskless asset, the sample tangency portfolio, and the sample global minimum-variance portfolio dominates a portfolio with just the riskless asset and the sample tangency portfolio, suggesting that the presence of estimation risk completely alters the theoretical recommendation of a two-fund portfolio.

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44

Cheng, A. H.-D., and D. Ouazar. "Theis Solution Under Aquifer Parameter Uncertainty." Ground Water 33, no. 1 (January 1995): 11–15. http://dx.doi.org/10.1111/j.1745-6584.1995.tb00257.x.

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Briggs, Andrew H., Milton C. Weinstein, Elisabeth A. L. Fenwick, Jonathan Karnon, Mark J. Sculpher, and A. David Paltiel. "Model Parameter Estimation and Uncertainty Analysis." Medical Decision Making 32, no. 5 (September 2012): 722–32. http://dx.doi.org/10.1177/0272989x12458348.

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46

Traficante, Guido. "Monetary policy, parameter uncertainty and welfare." Journal of Macroeconomics 35 (March 2013): 73–80. http://dx.doi.org/10.1016/j.jmacro.2012.11.005.

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47

Ramos-Pedroza, N., W. MacKunis, and M. Reyhanoglu. "Synthetic Jet Actuator-Based Aircraft Tracking Using a Continuous Robust Nonlinear Control Strategy." International Journal of Aerospace Engineering 2017 (2017): 1–13. http://dx.doi.org/10.1155/2017/4934281.

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A robust nonlinear control law that achieves trajectory tracking control for unmanned aerial vehicles (UAVs) equipped with synthetic jet actuators (SJAs) is presented in this paper. A key challenge in the control design is that the dynamic characteristics of SJAs are nonlinear and contain parametric uncertainty. The challenge resulting from the uncertain SJA actuator parameters is mitigated via innovative algebraic manipulation in the tracking error system derivation along with a robust nonlinear control law employing constant SJA parameter estimates. A key contribution of the paper is a rigorous analysis of the range of SJA actuator parameter uncertainty within which asymptotic UAV trajectory tracking can be achieved. A rigorous stability analysis is carried out to prove semiglobal asymptotic trajectory tracking. Detailed simulation results are included to illustrate the effectiveness of the proposed control law in the presence of wind gusts and varying levels of SJA actuator parameter uncertainty.

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Yang, Zhi Chun, and Ying Song Gu. "Robust Flutter Analysis of an Airfoil with Flap Freeplay Uncertainty." Advanced Materials Research 33-37 (March 2008): 1247–52. http://dx.doi.org/10.4028/www.scientific.net/amr.33-37.1247.

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Modern robust flutter method is an advanced technique for flutter margin estimation. It always gives the worst-case flutter speed with respect to potential modeling errors. Most literatures are focused on linear parameter uncertainty in mass, stiffness and damping parameters, etc. But the uncertainties of some structural nonlinear parameters, the freeplay in control surface for example, have not been taken into account. A robust flutter analysis approach in μ-framework with uncertain nonlinear operator is proposed in this study. Using describing function method the equivalent stiffness formulation is derived for a two dimensional wing model with freeplay nonlinearity in its flap rotating stiffness. The robust flutter margin is calculated for the two dimensional wing with flap freeplay uncertainty and the results are compared with that obtained with nominal parameter values. It is found that by considering the perturbation of freeplay parameter more conservative flutter boundary can be obtained, and the proposed method in μ-framework can be applied in flutter analysis with other types of concentrated nonlinearities.

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49

Babaniyi, Olalekan, Ruanui Nicholson, Umberto Villa, and Noémi Petra. "Inferring the basal sliding coefficient field for the Stokes ice sheet model under rheological uncertainty." Cryosphere 15, no. 4 (April 9, 2021): 1731–50. http://dx.doi.org/10.5194/tc-15-1731-2021.

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Abstract. We consider the problem of inferring the basal sliding coefficient field for an uncertain Stokes ice sheet forward model from synthetic surface velocity measurements. The uncertainty in the forward model stems from unknown (or uncertain) auxiliary parameters (e.g., rheology parameters). This inverse problem is posed within the Bayesian framework, which provides a systematic means of quantifying uncertainty in the solution. To account for the associated model uncertainty (error), we employ the Bayesian approximation error (BAE) approach to approximately premarginalize simultaneously over both the noise in measurements and uncertainty in the forward model. We also carry out approximative posterior uncertainty quantification based on a linearization of the parameter-to-observable map centered at the maximum a posteriori (MAP) basal sliding coefficient estimate, i.e., by taking the Laplace approximation. The MAP estimate is found by minimizing the negative log posterior using an inexact Newton conjugate gradient method. The gradient and Hessian actions to vectors are efficiently computed using adjoints. Sampling from the approximate covariance is made tractable by invoking a low-rank approximation of the data misfit component of the Hessian. We study the performance of the BAE approach in the context of three numerical examples in two and three dimensions. For each example, the basal sliding coefficient field is the parameter of primary interest which we seek to infer, and the rheology parameters (e.g., the flow rate factor or the Glen's flow law exponent coefficient field) represent so-called nuisance (secondary uncertain) parameters. Our results indicate that accounting for model uncertainty stemming from the presence of nuisance parameters is crucial. Namely our findings suggest that using nominal values for these parameters, as is often done in practice, without taking into account the resulting modeling error, can lead to overconfident and heavily biased results. We also show that the BAE approach can be used to account for the additional model uncertainty at no additional cost at the online stage.

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50

Imholz, Maurice, Dirk Vandepitte, and David Moens. "Analysis of the Effect of Uncertain Clamping Stiffness on the Dynamical Behaviour of Structures Using Interval Field Methods." Applied Mechanics and Materials 807 (November 2015): 195–204. http://dx.doi.org/10.4028/www.scientific.net/amm.807.195.

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In uncertainty calculation, the inability of interval parameters to take into account mutual dependency is a major shortcoming. When parameters with a geometric perspective are involved, the construction of a model using intervals at discrete locations not only increases the problem dimensionality unnecessarily, but it also assumes no dependency whatsoever, including unrealistic parameter combinations leading to results that probably overestimate the true uncertainty. The concept of modelling uncertainty with a geometric aspect using interval fields eliminates this problem by defining basis functions and expressing the uncertain process as a weighted sum of these functions. The definition of the functions enables the model to take into account geometrically dependent parameters, whereas the coefficients in a non-interactive interval format represent the uncertainty. This paper introduces a new type of interval field specifically tailored for geometrically oriented uncertain parameters, based on a maximum gradient condition to model the dependency. This field definition is then applied to a model of a clamped plate with uncertain clamping stiffness with the purpose of identifying the effects of spatial variability and mean value separately.

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