Design of Experiments Using Uncertainty Information

1996 ◽  
Vol 118 (3) ◽  
pp. 532-538 ◽  
Author(s):  
A. F. Emery ◽  
T. D. Fadale
Keyword(s):  
Inverse Problem ◽  
Parameter Estimation ◽  
Design Of Experiments ◽  
Measurement Noise ◽  
Model Parameters ◽  
Maximum Information ◽  
Estimated Parameters ◽  
Uncertainty Information

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.

Utilizing the Ensemble Kalman Filter and Ensemble Kalman Smoother for Combined State and Parameter Estimation of a Three-Dimensional Towed Underwater Cable Model

2017 ◽  
Vol 139 (6) ◽  
Author(s):  
Jan Vidar Grindheim ◽  
Inge Revhaug ◽  
Egil Pedersen
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Three Dimensional ◽  
Ocean Current ◽  
Model Parameters ◽  
State Variables ◽  
Kalman Smoother ◽  
Estimated Parameters ◽  
Underwater Cables

A finite difference method (FDM) solving the coupled partial differential equations governing three-dimensional (3D) motions of a towed underwater cable has been implemented in a combined ensemble Kalman filter (EnKF) and ensemble Kalman smoother (EnKS), as a new approach to combined state and parameter estimation for towed underwater cables. A simulation study of the method applied to a seismic streamer has been performed. Cable state variables as well as model parameters are estimated. Parameters estimated are crossline ocean current varying with time as well as cable tangential drag coefficient. The presented results indicate that the method is able to estimate state as well as parameters for seismic streamers.

Improved Parameter Estimation by Noise Compensation in the Time-Scale Domain

2009 ◽  
Author(s):  
James R. McCusker ◽  
Todd Currier ◽  
Kourosh Danai
Keyword(s):  
Parameter Estimation ◽  
Dynamic Model ◽  
Time Scale ◽  
Prediction Error ◽  
Noise Suppression ◽  
Model Parameters ◽  
Individual Parameter ◽  
Noise Compensation ◽  
Confidence Factor ◽  
Estimated Parameters

It was shown recently that parameter estimation can be performed directly in the time-scale domain by isolating regions wherein the prediction error can be attributed to the error of individual dynamic model parameters [1]. Based on these single-parameter attributions of the prediction error, individual parameter errors can be estimated for iterative parameter estimation. A benefit of relying entirely on the time-scale domain for parameter estimation is the added capacity for noise suppression. This paper explores this benefit by introducing a noise compensation method that estimates the distortion by noise of the prediction error in the time-scale domain and incorporates it as a confidence factor when estimating individual parameter errors. This method is shown to further improve the estimated parameters beyond the time-filtering and denoising techniques developed for time-based estimation.

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.

scholarly journals Novel Optimization-Based Parameter Estimation Method for the Bass Diffusion Model

SAGE Open ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 215824402110269
Author(s):  
Lang Liang
Keyword(s):  
Parameter Estimation ◽  
Least Squares Method ◽  
Weighted Least Squares ◽  
Estimation Method ◽  
Reference Value ◽  
Diffusion Problem ◽  
Bass Model ◽  
Weighted Least Squares Method ◽  
Estimated Parameters ◽  
Bass Diffusion Model

The Bass model is the most popular model for forecasting the diffusion process of a new product. However, the controlling parameters in it are unknown in practice and need to be determined in advance. Currently, the estimation of the controlling parameters has been approached by various techniques. In this case, a novel optimization-based parameter estimation (OPE) method for the Bass model is proposed in the theoretical framework of system dynamics ( SD). To do this, the SD model of the Bass differential equation is first established and then the corresponding optimization mathematical model is formulated by introducing the controlling parameters as design variable and the discrepancy of the adopter function to the reference value as objective function. Using the VENSIM software, the present SD optimization model is solved, and its effectiveness and accuracy are demonstrated by two examples: one involves the exact solution and another is related to the actual user diffusion problem from Chinese Mobile. The results show that the present OPE method can produce higher predicting accuracy of the controlling parameters than the nonlinear weighted least squares method and the genetic algorithms. Moreover, the reliability interval of the estimated parameters and the goodness of fitting of the optimal results are given as well to further demonstrate the accuracy of the present OPE method.

scholarly journals Determination of synchronous generator nonlinear model parameters based on power rejection tests using a gradient optimization algorithm

2017 ◽  
Vol 65 (4) ◽  
pp. 479-488 ◽  
Author(s):  
A. Boboń ◽  
A. Nocoń ◽  
S. Paszek ◽  
P. Pruski
Keyword(s):  
Parameter Estimation ◽  
Objective Function ◽  
Optimization Algorithm ◽  
Least Squares Method ◽  
Synchronous Generator ◽  
Operating Conditions ◽  
Model Parameters ◽  
State Variables ◽  
Starting Point ◽  
Gradient Optimization

AbstractThe paper presents a method for determining electromagnetic parameters of different synchronous generator models based on dynamic waveforms measured at power rejection. Such a test can be performed safely under normal operating conditions of a generator working in a power plant. A generator model was investigated, expressed by reactances and time constants of steady, transient, and subtransient state in the d and q axes, as well as the circuit models (type (3,3) and (2,2)) expressed by resistances and inductances of stator, excitation, and equivalent rotor damping circuits windings. All these models approximately take into account the influence of magnetic core saturation. The least squares method was used for parameter estimation. There was minimized the objective function defined as the mean square error between the measured waveforms and the waveforms calculated based on the mathematical models. A method of determining the initial values of those state variables which also depend on the searched parameters is presented. To minimize the objective function, a gradient optimization algorithm finding local minima for a selected starting point was used. To get closer to the global minimum, calculations were repeated many times, taking into account the inequality constraints for the searched parameters. The paper presents the parameter estimation results and a comparison of the waveforms measured and calculated based on the final parameters for 200 MW and 50 MW turbogenerators.

scholarly journals Non-Stationary Model of Cerebral Oxygen Transport with Unknown Sources

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 910
Author(s):  
Andrey Kovtanyuk ◽  
Alexander Chebotarev ◽  
Varvara Turova ◽  
Irina Sidorenko ◽  
Renée Lampe
Keyword(s):  
Inverse Problem ◽  
Oxygen Transport ◽  
Model Parameters ◽  
Cerebral Oxygen ◽  
System Of Equations ◽  
Blood Oxygen ◽  
Stationary Model ◽  
Average Oxygen Concentration ◽  
The Right ◽  
The Brain

An inverse problem for a system of equations modeling oxygen transport in the brain is studied. The problem consists of finding the right-hand side of the equation for the blood oxygen transport, which is a linear combination of given functionals describing the average oxygen concentration in the neighborhoods of the ends of arterioles and venules. The overdetermination condition is determined by the values of these functionals evaluated on the solution. The unique solvability of the problem is proven without any smallness assumptions on the model parameters.

scholarly journals Bayesian Reconstruction through Adaptive Image Notion

Proceedings ◽  
2019 ◽  
Vol 33 (1) ◽  
pp. 21
Author(s):  
Fabrizia Guglielmetti ◽  
Eric Villard ◽  
Ed Fomalont
Keyword(s):  
Inverse Problem ◽  
Image Plane ◽  
Source Distribution ◽  
Bayesian Probability ◽  
Model Parameters ◽  
Uncertain Information ◽  
Source Detection ◽  
Component Mixture ◽  
Ill Posed ◽  
Image Planes

A stable and unique solution to the ill-posed inverse problem in radio synthesis image analysis is sought employing Bayesian probability theory combined with a probabilistic two-component mixture model. The solution of the ill-posed inverse problem is given by inferring the values of model parameters defined to describe completely the physical system arised by the data. The analysed data are calibrated visibilities, Fourier transformed from the ( u , v ) to image planes. Adaptive splines are explored to model the cumbersome background model corrupted by the largely varying dirty beam in the image plane. The de-convolution process of the dirty image from the dirty beam is tackled in probability space. Probability maps in source detection at several resolution values quantify the acquired knowledge on the celestial source distribution from a given state of information. The information available are data constrains, prior knowledge and uncertain information. The novel algorithm has the aim to provide an alternative imaging task for the use of the Atacama Large Millimeter/Submillimeter Array (ALMA) in support of the widely used Common Astronomy Software Applications (CASA) enhancing the capabilities in source detection.

scholarly journals Simultaneous estimation of land surface scheme states and parameters using the ensemble Kalman filter: identical twin experiments

2011 ◽  
Vol 15 (8) ◽  
pp. 2437-2457 ◽  
Author(s):  
S. Nie ◽  
J. Zhu ◽  
Y. Luo
Keyword(s):  
Parameter Estimation ◽  
Soil Moisture ◽  
Kalman Filter ◽  
Ensemble Kalman Filter ◽  
Land Surface ◽  
Estimation Method ◽  
State Parameter ◽  
Hydraulic Parameters ◽  
Constrained Estimation ◽  
Estimated Parameters

Abstract. The performance of the ensemble Kalman filter (EnKF) in soil moisture assimilation applications is investigated in the context of simultaneous state-parameter estimation in the presence of uncertainties from model parameters, soil moisture initial condition and atmospheric forcing. A physically based land surface model is used for this purpose. Using a series of identical twin experiments in two kinds of initial parameter distribution (IPD) scenarios, the narrow IPD (NIPD) scenario and the wide IPD (WIPD) scenario, model-generated near surface soil moisture observations are assimilated to estimate soil moisture state and three hydraulic parameters (the saturated hydraulic conductivity, the saturated soil moisture suction and a soil texture empirical parameter) in the model. The estimation of single imperfect parameter is successful with the ensemble mean value of all three estimated parameters converging to their true values respectively in both NIPD and WIPD scenarios. Increasing the number of imperfect parameters leads to a decline in the estimation performance. A wide initial distribution of estimated parameters can produce improved simultaneous multi-parameter estimation performances compared to that of the NIPD scenario. However, when the number of estimated parameters increased to three, not all parameters were estimated successfully for both NIPD and WIPD scenarios. By introducing constraints between estimated hydraulic parameters, the performance of the constrained three-parameter estimation was successful, even if temporally sparse observations were available for assimilation. The constrained estimation method can reduce RMSE much more in soil moisture forecasting compared to the non-constrained estimation method and traditional non-parameter-estimation assimilation method. The benefit of this method in estimating all imperfect parameters simultaneously can be fully demonstrated when the corresponding non-constrained estimation method displays a relatively poor parameter estimation performance. Because all these constraints between parameters were obtained in a statistical sense, this constrained state-parameter estimation scheme is likely suitable for other land surface models even with more imperfect parameters estimated in soil moisture assimilation applications.

scholarly journals Inverse distributed hydrological modelling of Alpine catchments

2006 ◽  
Vol 10 (3) ◽  
pp. 395-412 ◽  
Author(s):  
H. Kunstmann ◽  
J. Krause ◽  
S. Mayr
Keyword(s):  
Parameter Estimation ◽  
Hydrological Model ◽  
Model Performance ◽  
Horizontal Resolution ◽  
Nonlinear Parameter ◽  
Model Complexity ◽  
Distributed Hydrological Model ◽  
Nonlinear Parameter Estimation ◽  
Estimated Parameters ◽  
Physically Based

Abstract. Even in physically based distributed hydrological models, various remaining parameters must be estimated for each sub-catchment. This can involve tremendous effort, especially when the number of sub-catchments is large and the applied hydrological model is computationally expensive. Automatic parameter estimation tools can significantly facilitate the calibration process. Hence, we combined the nonlinear parameter estimation tool PEST with the distributed hydrological model WaSiM. PEST is based on the Gauss-Marquardt-Levenberg method, a gradient-based nonlinear parameter estimation algorithm. WaSiM is a fully distributed hydrological model using physically based algorithms for most of the process descriptions. WaSiM was applied to the alpine/prealpine Ammer River catchment (southern Germany, 710 km2 in a 100×100 m2 horizontal resolution. The catchment is heterogeneous in terms of geology, pedology and land use and shows a complex orography (the difference of elevation is around 1600 m). Using the developed PEST-WaSiM interface, the hydrological model was calibrated by comparing simulated and observed runoff at eight gauges for the hydrologic year 1997 and validated for the hydrologic year 1993. For each sub-catchment four parameters had to be calibrated: the recession constants of direct runoff and interflow, the drainage density, and the hydraulic conductivity of the uppermost aquifer. Additionally, five snowmelt specific parameters were adjusted for the entire catchment. Altogether, 37 parameters had to be calibrated. Additional a priori information (e.g. from flood hydrograph analysis) narrowed the parameter space of the solutions and improved the non-uniqueness of the fitted values. A reasonable quality of fit was achieved. Discrepancies between modelled and observed runoff were also due to the small number of meteorological stations and corresponding interpolation artefacts in the orographically complex terrain. Application of a 2-dimensional numerical groundwater model partly yielded a slight decrease of overall model performance when compared to a simple conceptual groundwater approach. Increased model complexity therefore did not yield in general increased model performance. A detailed covariance analysis was performed allowing to derive confidence bounds for all estimated parameters. The correlation between the estimated parameters was in most cases negligible, showing that parameters were estimated independently from each other.

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