scholarly journals Parameter Estimation of Partially Observed Turbulent Systems Using Conditional Gaussian Path-Wise Sampler

Computation ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 91
Author(s):  
Ziheng Zhang ◽  
Nan Chen
Keyword(s):  
Parameter Estimation ◽  
Sampling Method ◽  
Data Augmentation ◽  
Iteration Algorithm ◽  
Model Parameters ◽  
Unknown Parameters ◽  
Partial Observations ◽  
Highly Nonlinear ◽  
Partially Observed ◽  
Non Gaussian

Parameter estimation of complex nonlinear turbulent dynamical systems using only partially observed time series is a challenging topic. The nonlinearity and partial observations often impede using closed analytic formulae to recover the model parameters. In this paper, an exact path-wise sampling method is developed, which is incorporated into a Bayesian Markov chain Monte Carlo (MCMC) algorithm in light of data augmentation to efficiently estimate the parameters in a rich class of nonlinear and non-Gaussian turbulent systems using partial observations. This path-wise sampling method exploits closed analytic formulae to sample the trajectories of the unobserved variables, which avoid the numerical errors in the general sampling approaches and significantly increase the overall parameter estimation efficiency. The unknown parameters and the missing trajectories are estimated in an alternating fashion in an adaptive MCMC iteration algorithm with rapid convergence. It is shown based on the noisy Lorenz 63 model and a stochastically coupled FitzHugh–Nagumo model that the new algorithm is very skillful in estimating the parameters in highly nonlinear turbulent models. The model with the estimated parameters succeeds in recovering the nonlinear and non-Gaussian features of the truth, including capturing the intermittency and extreme events, in both test examples.

scholarly journals Can Short and Partial Observations Reduce Model Error and Facilitate Machine Learning Prediction?

Entropy ◽  
2020 ◽  
Vol 22 (10) ◽  
pp. 1075
Author(s):  
Nan Chen
Keyword(s):  
Machine Learning ◽  
Model Error ◽  
Machine Learning Algorithms ◽  
Training Data ◽  
Conditional Sampling ◽  
Data Set ◽  
Partial Observations ◽  
Sampling Algorithm ◽  
Highly Nonlinear ◽  
Non Gaussian

Predicting complex nonlinear turbulent dynamical systems is an important and practical topic. However, due to the lack of a complete understanding of nature, the ubiquitous model error may greatly affect the prediction performance. Machine learning algorithms can overcome the model error, but they are often impeded by inadequate and partial observations in predicting nature. In this article, an efficient and dynamically consistent conditional sampling algorithm is developed, which incorporates the conditional path-wise temporal dependence into a two-step forward-backward data assimilation procedure to sample multiple distinct nonlinear time series conditioned on short and partial observations using an imperfect model. The resulting sampled trajectories succeed in reducing the model error and greatly enrich the training data set for machine learning forecasts. For a rich class of nonlinear and non-Gaussian systems, the conditional sampling is carried out by solving a simple stochastic differential equation, which is computationally efficient and accurate. The sampling algorithm is applied to create massive training data of multiscale compressible shallow water flows from highly nonlinear and indirect observations. The resulting machine learning prediction significantly outweighs the imperfect model forecast. The sampling algorithm also facilitates the machine learning forecast of a highly non-Gaussian climate phenomenon using extremely short observations.

Parameter estimation of single diode PV module based on Nelder-Mead optimization algorithm

2018 ◽  
Vol 15 (1) ◽  
pp. 70-81 ◽  
Author(s):  
Alivarani Mohapatra ◽  
Byamakesh Nayak ◽  
Kanungo Barada Mohanty
Keyword(s):  
Parameter Estimation ◽  
Optimization Algorithm ◽  
Environmental Conditions ◽  
Reference Model ◽  
Model Parameters ◽  
Unknown Parameters ◽  
Pv System ◽  
Content Type ◽  
Pv Module ◽  
Proposed Model

Purpose This paper aims to propose a simple, derivative-free novel method named as Nelder–Mead optimization algorithm to estimate the unknown parameters of the photovoltaic (PV) module considering the environmental conditions. Design/methodology/approach At a particular temperature and irradiation, experimental current-voltage (I-V) and power-voltage (P-V) characteristics are drawn and considered as a reference model. The PV system model with unknown model parameters is considered as the adaptive model whose unknown model parameters are to be adapted so that the simulated characteristics closely matches with the experimental characteristics. A single diode (Rsh) model with five unknown model parameters is considered here for the parameter estimation. Findings The key advantages of this method are that parameters are estimated considering environmental conditions. Experimental characteristics are considered for parameter estimation which gives accurate results. Parameters are estimated considering both I-V and P-V curves as most of the applications demand extraction of the actual power from the PV module. Originality/value The proposed model is compared with other three well-known models available in the literature considering various statistical errors. The results show the superiority of the proposed model with a minimum error for both I-V and P-V characteristics.

Bayesian Information Fusion of Multmodality Nondestructive Measurements for Probabilistic Mechanical Property Estimation

2020 ◽  
Author(s):  
Jie Chen ◽  
Yongming Liu
Keyword(s):  
Bayesian Inference ◽  
Missing Data ◽  
Data Augmentation ◽  
Engineering Application ◽  
Predictive Performance ◽  
Model Parameters ◽  
Unknown Parameters ◽  
Reinforcing Bar ◽  
Input Dataset ◽  
Nondestructive Measurements

Abstract Missing data occur when no data value is available for the variable in an observation. In this research, Bayesian data augmentation method is adopted and implemented for prediction with missing data. The data augmentation process is conducted through Bayesian inference with missing data assuming the multivariate normal distribution. Gibbs sampling is used to draw posterior simulations of the joint distribution of unknown parameters and unobserved quantities. The missing elements of the data are sampled conditional on the observed elements. The distribution of model parameters and variables with missing data can be obtained for reliability analysis. Two examples are given to illustrate the engineering application of Bayesian inference with missing data. The first example is to predict the yield strength of aging pipeline by fusing the incomplete surface information with missing data. The predictive performance is compared among direct surface indentation technique, linear regression with complete data and Bayesian inference with missing data. The second example is to predict the fatigue life of corroded steel reinforcing bar from the incomplete input dataset. The predicted fatigue lives are compared with experimental data. Both examples demonstrate that the Bayesian method can deal with missing data problem properly and show good predictive performance.

scholarly journals Hydrologic forecasting using artificial neural networks: a Bayesian sequential Monte Carlo approach

2010 ◽  
Vol 13 (1) ◽  
pp. 25-35 ◽  
Author(s):  
Kuo-Lin Hsu
Keyword(s):  
Monte Carlo ◽  
Parameter Estimation ◽  
Sequential Monte Carlo ◽  
Model Parameters ◽  
Ann Model ◽  
Streamflow Prediction ◽  
Streamflow Estimation ◽  
Artificial Neural ◽  
Artificial Neural Network Ann ◽  
Non Gaussian

Sequential Monte Carlo (SMC) methods are known to be very effective for the state and parameter estimation of nonlinear and non-Gaussian systems. In this study, SMC is applied to the parameter estimation of an artificial neural network (ANN) model for streamflow prediction of a watershed. Through SMC simulation, the probability distribution of model parameters and streamflow estimation is calculated. The results also showed the SMC approach is capable of providing reliable streamflow prediction under limited available observations.

scholarly journals Application of ensemble transform data assimilation methods for parameter estimation in nonlinear problems

2018 ◽  
Author(s):  
Sangeetika Ruchi ◽  
Svetlana Dubinkina
Keyword(s):  
Parameter Estimation ◽  
Data Assimilation ◽  
Nonlinear Problems ◽  
Model Parameters ◽  
Ensemble Size ◽  
Uncertain Model ◽  
Initial Ensemble ◽  
Non Gaussian ◽  
Posterior Estimation ◽  
Ensemble Transform

Abstract. Over the years data assimilation methods have been developed to obtain estimations of uncertain model parameters by taking into account a few observations of a model state. However, most of these computationally affordable methods have assumptions of Gaussianity, e.g. an Ensemble Kalman Filter. Ensemble Transform Particle Filter does not have the assumption of Gaussianity and has proven to be highly beneficial for an initial condition estimation and a small number of parameter estimation in chaotic dynamical systems with non-Gaussian distributions. In this paper we employ Ensemble Transform Particle Smoother (ETPS) and Ensemble Transform Kalman Smoother (ETKS) for parameter estimation in nonlinear problems with 1, 5, and 2500 uncertain parameters and compare them to importance sampling (IS). We prove that the updated parameters obtained by ETPS lie within the range of an initial ensemble, which is not the case for ETKS. We examine the performance of ETPS and ETKS in a twin experiment setup, where observations of pressure are synthetically created based on the know values of parameters. The numerical experiments demonstrate that the ETKS provides good estimations of the mean parameters but not of the posterior distributions and as the ensemble size increases the posterior does not improve. ETPS provides good approximations of the posterior and as the ensemble size increases the posterior converges to the posterior obtained by IS with a large ensemble. ETKS is very robust while ETPS is very sensitive with respect to the initial ensemble. An issue of an increase in the root mean square error after data assimilation is performed in ETPS for a high-dimensional test problem is resolved by applying distance-based localization, which however deteriorated the posterior estimation.

scholarly journals A Bayesian dose-finding design for outcomes evaluated with uncertainty

2021 ◽  
pp. 174077452110015
Author(s):  
Matthew J Schipper ◽  
Ying Yuan ◽  
Jeremy MG Taylor ◽  
Randall K Ten Haken ◽  
Christina Tsien ◽  
...  
Keyword(s):  
Phase I ◽  
Phase I Trial ◽  
Data Augmentation ◽  
Maximum Tolerated Dose ◽  
Dose Finding ◽  
Continual Reassessment Method ◽  
Number Of Patients ◽  
Continual Reassessment ◽  
Partially Observed ◽  
Dose Limiting Toxicity

Introduction: In some phase I trial settings, there is uncertainty in assessing whether a given patient meets the criteria for dose-limiting toxicity. Methods: We present a design which accommodates dose-limiting toxicity outcomes that are assessed with uncertainty for some patients. Our approach could be utilized in many available phase I trial designs, but we focus on the continual reassessment method due to its popularity. We assume that for some patients, instead of the usual binary dose-limiting toxicity outcome, we observe a physician-assessed probability of dose-limiting toxicity specific to a given patient. Data augmentation is used to estimate the posterior probabilities of dose-limiting toxicity at each dose level based on both the fully observed and partially observed patient outcomes. A simulation study is used to assess the performance of the design relative to using the continual reassessment method on the true dose-limiting toxicity outcomes (available in simulation setting only) and relative to simple thresholding approaches. Results: Among the designs utilizing the partially observed outcomes, our proposed design has the best overall performance in terms of probability of selecting correct maximum tolerated dose and number of patients treated at the maximum tolerated dose. Conclusion: Incorporating uncertainty in dose-limiting toxicity assessment can improve the performance of the continual reassessment method design.

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.

Centered error entropy Kalman filter with application to satellite attitude determination

2021 ◽  
pp. 014233122110198
Author(s):  
Baojian Yang ◽  
Lu Cao ◽  
Dechao Ran ◽  
Bing Xiao
Keyword(s):  
Kalman Filter ◽  
Gaussian Noise ◽  
Attitude Determination ◽  
Complexity Analysis ◽  
Iteration Algorithm ◽  
Robust Algorithms ◽  
Convergence Conditions ◽  
Satellite Attitude ◽  
Heavy Tailed ◽  
Non Gaussian

Due to unavoidable factors, heavy-tailed noise appears in satellite attitude estimation. Traditional Kalman filter is prone to performance degradation and even filtering divergence when facing non-Gaussian noise. The existing robust algorithms have limited accuracy. To improve the attitude determination accuracy under non-Gaussian noise, we use the centered error entropy (CEE) criterion to derive a new filter named centered error entropy Kalman filter (CEEKF). CEEKF is formed by maximizing the CEE cost function. In the CEEKF algorithm, the prior state values are transmitted the same as the classical Kalman filter, and the posterior states are calculated by the fixed-point iteration method. The CEE EKF (CEE-EKF) algorithm is also derived to improve filtering accuracy in the case of the nonlinear system. We also give the convergence conditions of the iteration algorithm and the computational complexity analysis of CEEKF. The results of the two simulation examples validate the robustness of the algorithm we presented.

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 Genetic parameters for test-day model with random regressions for production traits of Czech Holstein cattle

2011 ◽  
Vol 50 (No. 4) ◽  
pp. 142-154 ◽  
Author(s):  
L. Zavadilová ◽  
J. Jamrozik ◽  
Schaeffer LR
Keyword(s):  
Milk Fat ◽  
Sampling Method ◽  
Random Regression ◽  
Model Parameters ◽  
Residual Variance ◽  
Posterior Distributions ◽  
Production Traits ◽  
Multiple Trait ◽  
Holstein Breed ◽  
Random Regression Model

Multiple-lactation random regression model was applied to test-day records of milk, fat and protein yields in the first three lactations of the Czech Holstein breed. Data included 9 583 cows, 89 584, 44 207 and 11 266 test-day records in the first, second and third lactation, respectively. Milk, fat and protein in the first three lactations were analysed separately and in a multiple-trait analysis. Linear model included herd-test date, fixed regressions within age-season class and two random effects: animal genetic and permanent environment modelled by regressions. Gibbs sampling method was used to generate samples from marginal posterior distributions of the model parameters. The single- and multiple-trait models provided similar results. Genetic and permanent environmental variances and heritability for particular days in milk were high at the beginning and at the end of lactation. The residual variance decreased throughout the lactation. The resulting heritability ranged from 0.13 to 0.52 and increased with parity.  

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