Model Parameter Estimation Problem Research Articles

Optimal model parameter estimation and performance analysis of PEM electrolyzer using modified honey badger algorithm

The electrochemical model of a proton exchange membrane (PEM) electrolyzer consists of a set of different unknown parameters, and identification of these parameters is needed. However, obtaining the optimum values of these parameters is critical, and this involves a complex, multi-variate, non-linear, and multimodal optimisation problem. In this article, a novel model parameter estimation problem for a PEM electrolyzer with eight unknown model parameters is formulated and solved using modified honey badger algorithm (MHBA). A mean squared error-based objective function is formulated and considered as the mean squared error (MSE) between the experimental voltage and the estimated voltage using MHBA algorithm. The accuracy of the proposed model is validated using polarization curves (J-V curve). It is found that the MHBA outperforms with a good mapping between experimental and estimated voltage. Also, the reliability and robustness for parameter estimation algorithm is validated considering two case studies with four different operating conditions. Additionally, the results obtained using MHBA are compared to those obtained with other competing algorithms. A statistical study including different statistical indices is also carried out to prove the robustness for the proposed approach. The results show that the minimum obtained values of MSE for different operating conditions are 8.73E-06, 8.75E-06, 6.17E-05 and 6.44E-05. Box plot study and convergence curves have also been drawn to check the effectiveness of the algorithm. Furthermore, to prove the superiority of the proposed approach, the PEM electrolyzer's performance is explored at different operating conditions, such as operating temperatures and output hydrogen pressures.

Maximum Likelihood Estimation in Mixed Integer Linear Models.

We consider the maximum likelihood (ML) parameter estimation problem for mixed integer linear models with arbitrary noise covariance. This problem appears in applications such as single frequency estimation, phase contrast imaging, and direction of arrival (DoA) estimation. Parameter estimates are found by solving a closest lattice point problem, which requires a lattice basis. In this letter, we present a lattice basis construction for ML parameter estimation and conclude with simulated results from DoA estimation and phase contrast imaging.

Superresolution Composite SAR Imaging Method by Hierarchical Pattern With Attributed Scattering Priors

Compared with the ideal point scattering model, the attributed scattering center (ASC) model provides concise and physically relevant description of the man-made targets, such as the vehicles and ships, giving an efficient way to interpret the measurements of high-frequency and wide-angle synthetic aperture radar (SAR). Since the ASC model is complicated, it gives rise to a high-dimensional model parameter estimation problem, leading to a heavy computational burden. Aimed at this problem, in this article, a novel superresolution composite SAR imaging algorithm is proposed based on sparse representation, in which the ASC attributes are estimated by a hierarchical pattern for reducing the computational cost. In the proposed algorithm, the ASC model parameters, classified into three categories, are estimated coarsely via minimum variance pursuit (MVP). Then these coarse estimates are refined jointly using the consensus alternating direction method of multipliers (CADMM) optimization for polarimetric measurements. The spectrum extrapolation and replacement are performed for superresolution and reducing the impact of model mismatch, followed by a fast Fourier transform (FFT)-based operation to efficiently obtain the final superresolution image. The proposed approach not only possesses the ability of superresolution reconstruction with the target nonideal scattering features’ enhancement but also offers the physically relevant attributes on the premise of estimation accuracy improvement and calculation capacity reduction. Extensive experiments are conducted to corroborate the effectiveness of the proposed algorithm.

Finite-time parameter estimation for an online monitoring of transformer: A system identification perspective

The effective online monitoring of thermal performance is the principal criterion that determines the Loss-of-Life (LoL), ageing rate, and loading capability of the transformer. To assess transformer thermal performance and life expectancy, Top-oil Temperature (TOT) and Hot spot Temperature (HST) should be accurately estimated. In general, the first-principle approach with a thermal-electrical analogy is used for the first-order dynamical model based on the Resistance-Capacitance (RC) circuit structure to approximate the evolution of thermal performance. Traditionally, the TOT model parameters are identified by looking for the input-output data that minimize the error between estimated and actual values. The Gradient Estimator (GE) based on the least-square minimization principle ensures the parameter convergence to their actual value and the parametric estimation error to zero only when the regressor (information vector) signals fulfill the stringent Persistence of Excitation (PE) condition. As the choice of input-output data plays crucial role in parameter estimation, the Design of Experiment (DoE) is generally conducted in the laboratory to satisfy the PE condition. Therefore, the TOT model parameter estimation problem is reformulated from a system identification perspective by exploring the finite-time estimators (FTEs) that accurately identify and estimate the TOT model parameters for the streaming data from real-time working transformers without any laboratory experiments and DoE. The experimental analysis on the sufficiency of data for parameter convergence is carried out on MATLAB to demonstrate the identified PE problem, the effect of DoE, and the performance of finite time estimators for real-time scenario based non-PE data in thermal modeling of the transformer.

A velocity-guided Harris hawks optimizer for function optimization and fault diagnosis of wind turbine.

Harris hawks optimizer (HHO) is a relatively novel meta-heuristic approach that mimics the behavior of Harris hawk over the process of predating the rabbits. The simplicity and easy implementation of HHO have attracted extensive attention of many researchers. However, owing to its capability to balance between exploration and exploitation is weak, HHO suffers from low precision and premature convergence. To tackle these disadvantages, an improved HHO called VGHHO is proposed by embedding three modifications. Firstly, a novel modified position search equation in exploitation phase is designed by introducing velocity operator and inertia weight to guide the search process. Then, a nonlinear escaping energy parameter E based on cosine function is presented to achieve a good transition from exploration phase to exploitation phase. Thereafter, a refraction-opposition-based learning mechanism is introduced to generate the promising solutions and helps the swarm to flee from the local optimal solution. The performance of VGHHO is evaluated on 18 classic benchmarks, 30 latest benchmark tests from CEC2017, 21 benchmark feature selection problems, fault diagnosis problem of wind turbine and PV model parameter estimation problem, respectively. The simulation results indicate that VHHO has higher solution quality and faster convergence speed than basic HHO and some well-known algorithms in the literature on most of the benchmark and real-world problems.

Vine copula mixture models and clustering for non-Gaussian data

The majority of finite mixture models suffer from not allowing asymmetric tail dependencies within components and not capturing non-elliptical clusters in clustering applications. Since vine copulas are very flexible in capturing these dependencies, a novel vine copula mixture model for continuous data is proposed. The model selection and parameter estimation problems are discussed, and further, a new model-based clustering algorithm is formulated. The use of vine copulas in clustering allows for a range of shapes and dependency structures for the clusters. The simulation experiments illustrate a significant gain in clustering accuracy when notably asymmetric tail dependencies or/and non-Gaussian margins within the components exist. The analysis of real data sets accompanies the proposed method. The model-based clustering algorithm with vine copula mixture models outperforms others, especially for the non-Gaussian multivariate data.

Robust parameter estimation with outlier-contaminated correlated measurements and applications to aerodynamic coefficient identification

We consider the robust parameter estimation problem for state-space models with correlated measurements in the presence of outliers. Both the scenarios that the statistical information of the nominal noises in state-space models is known or not are explored. A novel Kalman robust smoother is proposed via introducing a specific reweighting approach to estimate the system parameters as well as the states when the nominal noise covariances are known. For the case where the statistic information of the nominal noise is absent, a modified expectation–maximization algorithm is introduced and integrated into the proposed robust smoother for simultaneously estimating the unknown states, system parameters, and the noise covariances. The performance of the proposed methods is illustrated by solving the aerodynamic coefficient identification problem with the real flight data set. The simulation results reveal that the proposed approaches outperform several existing solutions when outliers occur in multiple components of correlated measurements.

Kinetic modeling of diesel autothermal reforming for fuel cell auxiliary power units

Fuel cell auxiliary power unit (FC-APU) system for heavy-duty trucks has been attracting much attention as an alternative to engine idling to reduce pollutant emissions. In this system, a reformer, which converts diesel, the main fuel of heavy-duty trucks, into syngas suitable for the fuel cell, is essential. A kinetic model of the reforming can be helpful in tasks such as the reactor design and system operation, but it is highly challenging to develop such a model due to the complexity of the reforming reaction network. Thus, in this study, we propose a systematic approach to build a reduced kinetic model of the diesel autothermal reformer. Specifically, microreactor experiments are conducted using a commercial diesel fuel, where the temperature, oxygen-to-carbon ratio (OCR), and steam-to-carbon ratio (SCR) are varied. Then, based on the composition measurements of the exit gas, optimal kinetic models are constructed by iteratively solving a parameter estimation problem for the candidate kinetic models with varying number of reactions. To reduce the number of candidates significantly, lumping techniques are used to generate reduced kinetic models. A stochastic optimization method is employed for the parameter estimation in which the concept of cross-entropy is used. The optimal reduced kinetic models with 3 and 4 reactions showed a consistency with the literature in terms of the reactions included. The accuracy of optimal reduced kinetic models increased, showing 21% improvement as the number of reactions increased from 3 to 4.

Maximum likelihood autoregressive model parameter estimation with noise corrupted independent snapshots

Maximum likelihood autoregressive (AR) model parameter estimation problem with independent snapshots observed under white Gaussian measurement noise is studied. In addition to the AR model parameters, the measurement noise variance is also included among the unknowns of the problem to develop a general solution covering several special cases such as the case of known noise variance, noise-free snapshots, the single snapshot operation etc. The presented solution is based on the expectation-maximization method which is formulated by assigning the noise-free snapshots as the missing data. An approximate version of the suggested method, at a significantly reduced computational load with virtually no loss of performance, has also been developed. Numerical results indicate that the suggested solution brings major performance improvements in terms of estimation accuracy and does not suffer from unstable AR filter estimates unlike some other methods in the literature. The suggested method can be especially useful for small-dimensional multiple-snapshot noisy AR modeling applications such as the clutter power spectrum modeling application in radar signal processing.

EQUIVALENT MODELS FOR PHOTOVOLTAIC CELL – A REVIEW

Over the years, the contribution of photovoltaic energy to an eco-friendly world is continually increasing. Photovoltaic (PV) cells are commonly modelled as circuits, so finding the appropriate circuit model parameters of PV cells is crucial for performance evaluation, control, efficiency computations and maximum power point tracking of solar PV systems. The problem of finding circuit model of solar PV cells is referred to as “PV cell equivalent model problem”. In this paper, the existing research works on PV cell model parameter estimation problem are classified according to error quali-quantitative analysis, number of parameters, translation equations and PV technology. The existent models were discussed pointing out its different levels of approximation. A qualitative comparative ranking was made and four models were found to be the best ones for simulating PV cells. Besides, based on the conducted review, some recommendations for future research are provided.

Optimization Method for the Evaluation of Convective Heat and Mass Transfer Effective Coefficients and Energy Sources in Drying Processes

A new optimization method for the assessment of the coefficients existing in a model of drying kinetics is developed and presented in this article. This method consists of matching the drying kinetics resulting from the mathematical model with the drying kinetics resulting from the experiments. Both the heat and mass transfer coefficients, the critical relative humidity, and the additional ultrasound energy (heat) source are included in the optimization procedure. The Adams–Bashforth multistep method of solving nonlinear ordinary differential equations is used. The inverse problem of model parameter estimation is solved by the Rosenbrock optimization method. The methodology is illustrated by the example of the ultrasound-assisted convective drying of apple and carrot. A high level of agreement between the results obtained experimentally and numerically was found. The obtained results confirmed the great influence of ultrasound on the drying kinetics. It was found that ultrasound application improved the mass transfer by 20–80% and heat transfer by 30–90%. It was also found that the heating effect caused by the ultrasound’s absorption was very small, with a value below 1%.

Efficient estimation of space varying parameters in numerical models using non-intrusive subdomain reduced order modeling

A reduced order modeling algorithm for the estimation of space varying parameter patterns in numerical models is proposed. In this approach domain decomposition is applied to construct separate approximations to the numerical model in every subdomain. We introduce a new local parameterization that decouples the computational cost of the algorithm from the number of global principal components and therefore provides attractive scaling for models with a very large number of uncertain parameter patterns. By defining uncertain parameter patterns only in the various subdomains the number of full order simulation required for the derivation of the reduced order models can be reduced drastically. To avoid non-smoothness at the boundaries of the subdomains, the optimal local parameters patterns are projected onto global parameter patterns. The computational effort of the new methodology hardly increases when the number of parameter patterns increases. The number of training models depends primarily on the maximum number of local parameters in a subdomain, which can be decreased by refining the domain decomposition. We apply the new algorithm to a large-scale reservoir model parameter estimation problem. In this application 282 parameters could be estimated using only 90 full order model runs.

Online Detection and Parameter Estimation With Correlated Observations

We present an online expectation maximization (EM) based algorithm for the problem of model parameter estimation and hypothesis testing based on observations from a network of heterogeneous sensors. The sensors’ measurements are assumed to be correlated and copula theory is used to model this correlation. Moreover, it is assumed that the statistical model for the sensors’ data is not completely known. We first develop the batch-mode EM to estimate the parameters of the underlying distributions of the sensors’ measurements and to detect the hypothesis. Next, we develop an online EM-based method that processes the data on a sample-by-sample basis. Numerical results are presented for both simulation data and two different real-world datasets. These results demonstrate the efficacy of the proposed method showing significant improvements for both parameter estimation and hypothesis testing compared to the method that ignores the correlation in sensors’ measurements. Hypothesis testing results from the real-world data are also compared with several unsupervised and supervised learning methods. It is shown that the proposed methods outperform the unsupervised and even some supervised methods.

Refraction-learning-based whale optimization algorithm for high-dimensional problems and parameter estimation of PV model

Whale optimization algorithm (WOA) is a relatively new meta-heuristic optimization algorithm which mimics the hunting behavior of humpback whales. This paper presents a modified version of WOA, called RLWOA, for solving high-dimensional optimization problems. The proposed RLWOA adopts a modified conversion parameter update rule that relies on Logistic model to balance between diversity and convergence during the search process, and a new refraction-learning strategy based on the principle of refraction of light is proposed to help the population jump out of a local optimum. The experiments on a set of benchmark test functions with various features, i.e., 12 widely used benchmark functions with 100, 1000, and 10000 dimensions, two practical engineering design problems, and parameter estimation problem of photovoltaic model. The comparisons demonstrate that the proposed RLWOA shows better or at least competitive performance against the standard WOA, WOA variants and other state-of-the-art meta-heuristic algorithms for solving high-dimensional numerical optimization, practical engineering design optimization, and photovoltaic model parameter estimation problems.

Model Predictive Control with Forward-Looking Persistent Excitation

This work deals with the dual-control problem of simultaneous regulation and model parameter estimation in model predictive control. We propose an adaptive model predictive control which guarantees a persistently exciting closed loop sequence by only looking forward in time into the prediction horizon. Earlier works needed to look backwards and preserve prior regressor data. With the new approach, under the assumption of a known periodic persistently exciting reference trajectory around the equilibrium, we demonstrate exponential convergence of nonlinear systems under the influence of the adaptive model predictive control combined with a recursive least squares identifier with forgetting factor despite bounded noise. The results are, at this stage, local in state and parameter estimate space.

A parametric lifetime model for a multicomponents system with spatial interactions

AbstractIn this paper, we consider a system made of n components displayed on a structure (eg, a steel plate). We define a parametric model for the hazard function, which includes covariates and spatial interaction between components. The state (nonfailed or failed) of each component is observed at some inspection times. From these data, we consider the problem of model parameter estimation. To achieve this, we suggest to use the SEM algorithm based on a pseudo‐likelihood function. A definition for the time‐to‐failure of the system is given, generalizing the classical cases. A study based on numerical simulations is provided to illustrate the proposed approach.

A history matching approach for calibrating hydrological models

Calibration of hydrological time-series models is a challenging task since these models give a wide spectrum of output series and calibration procedures require significant amount of time. From a statistical standpoint, this model parameter estimation problem simplifies to finding an inverse solution of a computer model that generates pre-specified time-series output (i.e., realistic output series). In this paper, we propose a modified history matching approach for calibrating the time-series rainfall-runoff models with respect to the real data collected from the state of Georgia, USA. We present the methodology and illustrate the application of the algorithm by carrying a simulation study and the two case studies. Several goodness-of-fit statistics were calculated to assess the model performance. The results showed that the proposed history matching algorithm led to a significant improvement, of 30% and 14% (in terms of root mean squared error) and 26% and 118% (in terms of peak percent threshold statistics), for the two case-studies with Matlab-Simulink and SWAT models, respectively.

Incremental Parameter Estimation under Rank-Deficient Measurement Conditions

The computation and modeling of extents has been proposed to handle the complexity of large-scale model identification tasks. Unfortunately, the existing extent-based framework only applies when certain conditions apply. Most typically, it is required that a unique value for each extent can be computed. This severely limits the applicability of this approach. In this work, we propose a novel procedure for parameter estimation inspired by the existing extent-based framework. A key difference with prior work is that the proposed procedure combines structural observability labeling, matrix factorization, and graph-based system partitioning to split the original model parameter estimation problem into parameter estimation problems with the least number of parameters. The value of the proposed method is demonstrated with an extensive simulation study and a study based on a historical data set collected to characterize the isomerization of α -pinene. Most importantly, the obtained results indicate that an important barrier to the application of extent-based frameworks for process modeling and monitoring tasks has been lifted.

Particle filters for inference of high-dimensional multivariate stochastic volatility models with cross-leverage effects

Multivariate stochastic volatility models are a popular and well-known class of models in the analysis of financial time series because of their abilities to capture the important stylized facts of financial returns data. We consider the problems of filtering distribution estimation and also marginal likelihood calculation for multivariate stochastic volatility models with cross-leverage effects in the high dimensional case, that is when the number of financial time series that we analyze simultaneously (denoted by $ d $) is large. The standard particle filter has been widely used in the literature to solve these intractable inference problems. It has excellent performance in low to moderate dimensions, but collapses in the high dimensional case. In this article, two new and advanced particle filters proposed in [4], named the space-time particle filter and the marginal space-time particle filter, are explored for these estimation problems. The better performance in both the accuracy and stability for the two advanced particle filters are shown using simulation and empirical studies in comparison with the standard particle filter. In addition, Bayesian static model parameter estimation problem is considered with the advances in particle Markov chain Monte Carlo methods. The particle marginal Metropolis-Hastings algorithm is applied together with the likelihood estimates from the space-time particle filter to infer the static model parameter successfully when that using the likelihood estimates from the standard particle filter fails.

Diffusion kurtosis imaging with free water elimination: A bayesian estimation approach.

PurposeDiffusion kurtosis imaging (DKI) is an advanced magnetic resonance imaging modality that is known to be sensitive to changes in the underlying microstructure of the brain. Image voxels in diffusion weighted images, however, are typically relatively large making them susceptible to partial volume effects, especially when part of the voxel contains cerebrospinal fluid. In this work, we introduce the “Diffusion Kurtosis Imaging with Free Water Elimination” (DKI‐FWE) model that separates the signal contributions of free water and tissue, where the latter is modeled using DKI.Theory and MethodsA theoretical study of the DKI‐FWE model, including an optimal experiment design and an evaluation of the relative goodness of fit, is carried out. To stabilize the ill‐conditioned estimation process, a Bayesian approach with a shrinkage prior (BSP) is proposed. In subsequent steps, the DKI‐FWE model and the BSP estimation approach are evaluated in terms of estimation error, both in simulation and real data experiments.ResultsAlthough it is shown that the DKI‐FWE model parameter estimation problem is ill‐conditioned, DKI‐FWE was found to describe the data significantly better compared to the standard DKI model for a large range of free water fractions. The acquisition protocol was optimized in terms of the maximally attainable precision of the DKI‐FWE model parameters. The BSP estimator is shown to provide reliable DKI‐FWE model parameter estimates.ConclusionThe combination of the DKI‐FWE model with BSP is shown to be a feasible approach to estimate DKI parameters, while simultaneously eliminating free water partial volume effects. Magn Reson Med 80:802–813, 2018. © 2018 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.