Parameter Estimation Techniques Research Articles

A Bayesian modelling approach for assessing non-stationarity in annual maximum rainfall under a changing climate

ABSTRACT Potential changes in hydro-meteorological events have been causing mass damage to the economy and lives. Among several other factors, the progression of climate change over a long time is expected to cause non-stationarity in annual maximum rainfall. Understanding the characteristics of annual maximum rainfall series is crucial for coastal cities as they are highly vulnerable due to the greatly varying weather patterns. In this paper, we propose stationary and non-stationary methods to model the effect of non-stationarity on the differing duration of annual maximum rainfall and demonstrate the impacts on nine coastal cities spread across the Arabian Sea and Bay of Bengal stretch of India. The Bayesian inference parameter estimation technique was used. It was found that while stationary models often fit well for longer-duration rainfall, non-stationary models often best fit the short duration.

Johnson–Schumacher Split-Plot Design Modelling of Rice Yield

Summary In this research, an intrinsically nonlinear split-plot design model (INSPDM) is formulated and studied. It was formulated by fitting a Johnson–Schumacher (JS) function to the split-plot model mean function. The fitted model parameters are estimated using the estimated generalized least squares (EGLS) technique based on a Gauss–Newton procedure with Taylor series expansion, by minimizing the objective function of the model. The variance components for the whole plot and subplot random effects are estimated using restricted maximum likelihood estimation (REML) techniques. The adequacy of the fitted INSPDM was tested using four median adequacy measures: resistant coefficient of determination, resistant prediction coefficient of determination, the resistant modeling efficiency statistic, and the median square error prediction statistic based on the residuals of the fitted model. Akaike’s Information Criterion (AIC), Corrected Akaike’s Information Criterion (AICC) and Bayesian Information Criterion (BIC) statistics are used to select the best parameter estimation technique. The results obtained are compared with the techniques of ordinary least squares (OLS) and EGLS via maximum likelihood estimation (MLE). The results showed the model to be adequate, reliable, stable, and a good fit based on EGLS-REML when compared with OLS and EGLS-MLE fitted model parameter estimates.

On the facile and accurate determination of the highly accurate recent methods to optimize the parameters of different fuel cells: Simulations and analysis

The proton exchange membrane fuel cell (PEMFC) is a potential source of renewable energy that offers a dual benefit of reducing environmental pollution and enabling easy electricity savings. The mathematical model of PEMFC involves several unknown parameters that need to be precisely estimated for developing an accurate model. This process of estimating parameters is known as the parameter estimation of PEMFC and is considered an optimization problem. Although the problem of parameter estimation for PEMFC belongs to the category of optimization problems, it cannot be solved by all optimization techniques as it is a complex and nonlinear problem. Therefore, this paper presents a new parameter estimation technique based on adopting a recently published metaheuristic algorithm known as the artificial hummingbird algorithm (AHA). AHA is simple and easy to implement as its main advantages encourage us to adopt it for tackling this problem. However, unfortunately, AHA suffers from slow convergence speed and hence will consume a huge number of function evaluations even reaching the desired outcomes. Therefore, two improvements have been applied to the classical AHA for proposing a new variant , namely IAHA, for overcoming the parameter estimation of PEMFC stacks. IAHA was applied to estimate the unknown parameters of six different PEMFC stacks and compared with 11 well-known competing optimizers in terms of accuracy of outcomes, convergence speed, stability, and CPU time. Based on the experimental results, IAHA outperforms all other algorithms across all performance parameters except for CPU time, which is on par with the other methods.

Impact of Shadow Economy on Sustainable Development in Africa

ABSTRACT This study contributes to the sustainable development literature by investigating the impact of the shadow economy on sustainable development in a panel of 30 African countries over a period of 2000–2017. The study employs parametric and nonparametric panel estimation techniques. The novel moment panel quantile regression method is also used to produce robust outcomes across the distribution of the explained variable in the presence of location shifters, scale variants, endogeneity, and outliers. The results reveal that the shadow economy reduces sustainable development in Africa. The study concludes that conscious efforts are needed to ensure that the shadow economy issue is addressed to enjoy the benefits of sustainable development in the African region.

VARMA model parameterization using MLLE approach for intraday wind power forecasting application

AbstractAccurate intraday wind power forecasting (WPF) is required by system operators to mitigate challenges arising from small‐scale grid integration of intermittent wind power. This low‐level integration of wind energy into the system urges quality deterministic forecast. Multivariate statistical models considering spatiotemporal correlations are commonly used for such WPF. However, prudent parameterization is a necessity to improve deterministic forecasts even in smaller datasets. This article proposes a computationally efficient vector autoregressive moving average (VARMA) based intraday WPF model that uses the novel maximum log‐likelihood estimation (MLLE) approach to estimate the best‐fit model parameters. MLLE approach reduces the spatiotemporal fitting error by approximately 15% with computational time deduction by more than 25%. Furthermore, an advanced accuracy in parameter estimation (AIPE) technique supports the MLLE approach to obtain the optimal training window length for computing distribution parameters with narrow confidence intervals. Proposed centralized forecast model is implemented on a group of Wind Farms (WFs) in SE Australia. Pre‐processing of wind power generation data is ensured using the Yeo–Johnson transformation and stationarity concept. Proposed model is accurate and computationally efficient as compared to benchmark models in terms of accuracy and computational time. An appreciated forecast quality is achieved using the proposed model having only 0.20 MW and 0.29 MW mean normalized RMSE for 3 and 10 WFs studies, respectively. Possible applicability of the proposed model includes an overall improvement in intraday decision‐making of wind energy producers and system operators.

Space-Vector State Dynamic Model of the SynRM Considering Self, Cross-Saturation and Iron Losses and Related Identification Technique

This paper proposes a space-vector dynamic model of the Synchronous Reluctance Motor (SynRM) including both self-saturation, cross-saturation effects, and iron losses. The model is expressed in state form, where the magnetizing current has been selected as a state variable. The proposed dynamic model is based on an original function between the stator flux and the magnetizing current components, improving a previously developed magnetic model. Additionally, the proposed model includes, besides the magnetic saturation, also iron losses. The proposed model requires 11 coefficients, among which 6 describe the self-saturation on both axes and 5 describe the cross-saturation. This paper presents also, from one side a technique for the estimation of the parameters of the magnetic model, and from the other side a purposely developed methodology for measuring the iron losses resistance as well as its variation with the speed and stator current amplitude. The proposed parameter estimation technique has been tested in both numerical simulation and experimentally on a suitably developed test set-up and the proposed model has been thus validated experimentally

On OAMP: Impact of the Orthogonal Principle

Approximate Message Passing (AMP) is an efficient iterative parameter-estimation technique for certain high-dimensional linear systems with non-Gaussian distributions, such as sparse systems. In AMP, a so-called Onsager term is added to keep estimation errors approximately Gaussian. Orthogonal AMP (OAMP) does not require this Onsager term, relying instead on an orthogonalization procedure to keep the current errors uncorrelated with (i.e., orthogonal to) past errors. In this paper, we show the generality and significance of the orthogonality in ensuring that errors are “asymptotically independently and identically distributed Gaussian” (AIIDG). This AIIDG property, which is essential for the attractive performance of OAMP, holds for separable functions. We present a simple and versatile procedure to establish the orthogonality through Gram-Schmidt (GS) orthogonalization, which is applicable to any prototype. We show that different AMP-type algorithms, such as expectation propagation (EP), turbo, AMP and OAMP, can be unified under the orthogonal principle. The simplicity and generality of OAMP provide efficient solutions for estimation problems beyond the classical linear models. As an example, we study the optimization of OAMP via the GS model and GS orthogonalization. More related applications will be discussed in a companion paper where new algorithms are developed for problems with multiple constraints and multiple measurement variables.

Bayesian Computational Technique for Modeling Caffeine Adsorption in a Fixed-Bed Column: Use of the Maximum Adsorption Capacity Deterministically and Experimental Design

This work applied a Bayesian computational technique for parameter estimation of adsorption breakthrough curve models with experimental data of caffeine (CAF) adsorption onto granular activated carbon (GAC). Different operational conditions were evaluated (volumetric flow: Q, adsorbent mass: W, and initial CAF concentration: C0) by a two-level factorial experimental design (23) to determine the best operational conditions. The models (Thomas, Yoon–Nelson, Yan, Clark, Gompertz, and Log-Gompertz) were fitted to the experimental data, estimating and not estimating the maximum adsorption capacity (qS). For model selection, five statistical metrics were calculated. The results showed that the proposed Bayesian technique, not estimating qS, was effective and all analyzed operational conditions obtained 95% of CAF removal. In the best condition, when qS reached 7.317 mgCAF/gGAC, the model that best adjusted the experimental data was Log-Gompertz, being suitable for practical approaches, and for its mechanisms, the Clark model best predicted the evaluated fixed-bed column.

Adapting to noise distribution shifts in flow-based gravitational-wave inference

Deep learning techniques for gravitational-wave parameter estimation have emerged as a fast alternative to standard samplers---producing results of comparable accuracy. These approaches (e.g., DINGO) enable amortized inference by training a normalizing flow to represent the Bayesian posterior conditional on observed data. By conditioning also on the noise power spectral density (PSD) they can even account for changing detector characteristics. However, training such networks requires knowing in advance the distribution of PSDs expected to be observed and therefore can only take place once all data to be analyzed have been gathered. Here, we develop a probabilistic model to forecast future PSDs, greatly increasing the temporal scope of trained deep learning models. Using PSDs from the second LIGO-Virgo observing run (O2)---plus just a single PSD from the beginning of the third (O3)---we show that we can train a DINGO network to perform accurate inference throughout O3 (on 37 real events). We therefore expect this approach to be a key component to enable the use of deep learning techniques for low-latency analyses of gravitational waves.

Adaptive Leader-Follower Consensus Control of Multiple Flexible Manipulators With Actuator Failures and Parameter Uncertainties

In this paper, the leader-follower consensus problem for a multiple flexible manipulator network with actuator failures, parameter uncertainties, and unknown time-varying boundary disturbances is addressed. The purpose of this study is to develop distributed controllers utilizing local interactive protocols that not only suppress the vibration of each flexible manipulator but also achieve consensus on joint angle position between actual followers and the virtual leader. Following the accomplishment of the reconstruction of the fault terms and parameter uncertainties, the adaptive neural network method and parameter estimation technique are employed to compensate for unknown items and bounded disturbances. Furthermore, the Lyapunov stability theory is used to demonstrate that followers' angle consensus errors and vibration deflections in closed-loop systems are uniformly ultimately bounded. Finally, the numerical simulation results confirm the efficacy of the proposed controllers.

A new optimum technique for parameter identification of the proton exchange membrane fuel cells based on improved remora optimizer

ABSTRACT The present study proposes a new parameter estimation technique for undefined parameters of proton exchange membrane fuel cell (PEMFC) stack models. To provide an efficient model identifier, an objective function by the Sum of Squared Error (SSE) between the empirical data and the predicted date of the PEM fuel cell stack has been employed, and the aim is to minimize this objective function. Here, a new improved design of Remora Optimizer is designed and used for the minimization purpose. The improved method has been improved by self-adaptive weighting for improving the convergence rate and for providing promising balance searching in both initial and next steps, and chaos mechanism for increasing the optimization process while keeping the exploration term based on pseudorandom values. The technique is used in two test cases and then a comparison of the results with several newest techniques is performed. Simulation results showed that the proposed IROA method with 2.05% and 0.019% error ratio for NedSstack PS6 and Horizon 500W PEMFC stack models, respectively, provides the best results compared with other comparative methods. Simulation achievements indicate that the presented approach has higher efficiency than the other compared methods.

Performance analysis of solar PV parameter estimation techniques

Firstly, this paper investigates the performances of the three different established parameter estimation techniques, namely multi-objective function, five-point metaheuristic, and hybrid-based approaches. Using these three different techniques, unknown model parameters, such as photovoltaic current (Ipv), dark saturation current (Io), series resistance (Rs), shunt resistance (Rsh), and Ideality factor (A), of mono-and poly-crystalline technology-based solar PV modules, are predicted. Afterwards, using the estimated unknown parameters and P-V &I-V characteristics curves, two different benchmarks, namely absolute relative maximum power error (ARMPE) and overall model error (OME), of these modules, are evaluated to reveal their best performances. In addition, various other parameter estimation techniques, such as iterative, analytical, curve-fitting, and metaheuristics-based methods, have also been considered for performance analysis. It is shown that the hybrid-based approach provides a better characterization than the other various established approaches. The value of %ARMPE is found almost zero with the hybrid approach for both modules. In addition, the smallest values of OME are obtained with the hybrid approach, i.e., 0.002 or 0.003 for poly- and 0.031 for the mono-crystalline technology-based solar PV module. Hence, a hybrid-based parameter estimation technique is suggested to achieve accurate characteristics of solar PV.

A novel technique for wall parameter estimation for through wall imaging systems

AbstractAccurate estimating of wall parameters is crucial for precisely locating targets and obtaining well‐focused through wall radar images. Recently, machine learning has been introduced for quick and precise estimation of wall parameters. One of the significant concerns with this approach is the generation of training and testing data, which require the fabrication of walls with different permittivity, thickness, and conductivity. Creating walls with varying permittivity, thickness, and conductivity can be difficult and expensive. Therefore, a cost‐effective method for estimating wall parameters is proposed in this paper. The proposed method uses an electromagnetic approach to train the artificial neural network to retrieve the relative permittivity and thickness of the wall. The proposed estimation approach has the advantages of high precision and low computational complexity. The performance of the proposed approach is validated on simulated and experimental data. The applicability of the proposed method has been shown with measured data from two real building walls. It is shown that the proposed method retrieved wall parameters with high accuracy.

Adaptive unscented Kalman filter for neuronal state and parameter estimation.

Data assimilation techniques for state and parameter estimation are frequently applied in the context of computational neuroscience. In this work, we show how an adaptive variant of the unscented Kalman filter (UKF) performs on the tracking of a conductance-based neuron model. Unlike standard recursive filter implementations, the robust adaptive unscented Kalman filter (RAUKF) jointly estimates the states and parameters of the neuronal model while adjusting noise covariance matrices online based on innovation and residual information. We benchmark the adaptive filter's performance against existing nonlinear Kalman filters and explore the sensitivity of the filter parameters to the system being modelled. To evaluate the robustness of the proposed solution, we simulate practical settings that challenge tracking performance, such as a model mismatch and measurement faults. Compared to standard variants of the Kalman filter the adaptive variant implemented here is more accurate and robust to faults.

A regional appraisal of electricity accessibility determinants: the relevance of international remittances, clean energy, income inequality, and institutional quality.

The majority of developing nations worldwide face severechallenges in ensuring universal electricity access for their respective populations. Hence, this study focuses on assessing the factors stimulating and inhibiting national electricity accessrates in 61 developing nations from six global regions during the 2000-2020 period. For analytical purposes, both parametric and non-parametric estimation techniques that are efficient in handling major panel data-related problems are used. Overall, the results reveal that a higher influx of remittances sent by the expatriates does not directlyinfluence electricity accessibility. However, adoption of clean energy and improvement in institutional quality promote electricity accessibility while higher income inequality undermines it. More importantly, good institutional quality mediates between international remittance receipts and electricity accessibility as results endorse that international remittance receipts and institutional quality improvement jointly exert electricity accessibility-promoting impacts. Moreover, these findings depict regional heterogeneity while the quantile-based analysis highlights contrasting impacts of international remittance receipts, clean energy use, and institutional quality across different quantiles of electricity accessibility. Contrarily, worsening incidences of income inequality are evidenced to undermine electricity accessibility across all quantiles. Therefore, considering these key findings, several electricity accessibility-boosting policies are suggested.

Discerning Discretization for Unmanned Underwater Vehicles DC Motor Control

Discretization is the process of converting a continuous function or model or equation into discrete steps. In this work, learning and adaptive techniques are implemented to control DC motors that are used for actuating control surfaces of unmanned underwater vehicles. Adaptive control is a strategy wherein the controller is designed to adapt the system with parameters that vary or are uncertain. Parameter estimation is the process of computing the parameters of a system using a model and measured data. Adaptive methods have been used in conjunction with different parameter estimation techniques. As opposed to the ubiquitous stochastic artificial intelligence approaches, very recently proposed deterministic artificial intelligence, a learning-based approach that uses the physics-defined process dynamics, is also applied to control the output of the DC motor to track a specified trajectory. This work goes further to evaluate the performance of the adaptive and learning techniques based on different discretization methods. The results are evaluated based on the absolute error mean between the output and the reference trajectory and the standard deviation of the error. The first-order hold method of discretization and surprisingly large sample time of seven-tenths of a second yields greater than sixty percent improvement over the results presented in the prequel literature.

Modeling and Parameter Estimation for Gas‐Phase Polyethylene Product Properties Using Dynamic and Steady‐State Data

AbstractModels are developed for gas‐phase ethylene/1‐hexene copolymerization using a 3‐site hafnocene catalyst. The models accurately predict joint molecular weight distribution and copolymer composition data for 15 semibatch lab‐scale copolymerization runs and 6 steady‐state pilot‐plant copolymerization runs, respectively. Kinetic rate constants and activation energies, which are common to both models, are estimated for the three types of active sites for each reaction in the kinetic scheme. Using parameter subset selection and estimation techniques, it is found that 34 of the 61 parameters should be estimated from the data. Incorporating the pilot‐plant data allow for estimation of two parameters, a deactivation rate constant and a β‐hydride elimination activation energy, that are not estimable using the lab‐scale data alone. At the 95% confidence level, 25 of the 34 parameters are significantly different than zero, which is more than the 19 significant parameter estimates obtained from the lab‐scale data alone. Good fits to the data are obtained, as are reliable predictions for a validation run not used in parameter estimation.

Lognormal seminumerical simulations of the Lyman α forest: comparison with full hydrodynamic simulations

ABSTRACTObservations of the Lyman α (Ly α) forest in spectra of distant quasars enable us to probe the matter power spectrum at relatively small scales. With several upcoming surveys, it is expected that there will be a many-fold increase in the quantity and quality of data, and hence it is important to develop efficient simulations to forward model these data sets. One such seminumerical method is based on the assumption that the baryonic densities in the intergalactic medium (IGM) follow a lognormal distribution. In this work, we test the robustness of the lognormal model of the Ly α forest in recovering a set of IGM parameters by comparing with high-resolution Sherwood smoothed particle hydrodynamics (SPH) simulations. We study the recovery of the parameters T0 (temperature of the mean-density IGM), γ (slope of the temperature–density relation), and Γ12 (hydrogen photoionization rate) at z ∼ 2.5 using a Markov chain Monte Carlo technique for parameter estimation. Using three flux statistics, the probability distribution, the mean flux, and the power spectrum, values of all three parameters, T0, γ, and Γ12, implied in the SPH simulations are recovered within 1 − σ (∼9, 4, and 1 per cent, respectively) of the median (best-fitting) values. We verify the validity of our results at different baryon smoothing filter, signal-to-noise ratio, box size and resolution, and data seed and confirm that the lognormal model can be used as an efficient tool for modelling the Ly α transmitted flux at z ∼ 2.5.

Optimal Parameter Estimation of Solar Photovoltaics Through Nature Inspired Metaheuristic and Hybrid Approaches

Estimation of solar photovoltaic (PV) equivalent model parameters through the manufacturer's datasheet or experimental performance current voltage (I-V) characteristics is an apprehension among researchers. In this paper, two approaches are instigated and compared i.e. metaheuristic pheromone value black widow optimisation (pv-BWO) and hybrid sailfish optimisation (h-SFO) for the estimation of a single-diode model (SDM) and double-diode model (DDM) parameters for the accurate solar PV modelling. Four distinct case studies that incorporate four different PV modules i.e. RTC France, PWP 201, SHARP ND-R250A5, and EIL 75W PV are investigated, where the validation of the proposed methods is carried out through the experimental performance characteristics of solar PV under test i.e. the I-V and power-voltage (P-V) performance characteristics. Moreover, the performance is evaluated on various error functions, and experimental I-V and P-V characteristics, where the results are also compared with the various techniques of parameter estimation in the literature. It is important to underline that the closeness of the objective function to zero exhibits the congruence of estimated parameters with the exact parameters, where the exact parameter value is not accessible. Therefore, the preciseness rests on the experimental data only, where any significant reduction in OF i.e. RMSE considered as an improvement towards the exactness of real unknown parameter values. The pv-BWO exhibits an average of 69.89% of lower error results when compared with few existing methods, whereas h-SFO recorded a higher RMSE of about 93% when compared with the pv-BWO which suggests the suitability of pv-BWO over h-SFO and few existing methods.

Speed-Controller-Independent Mechanical Parameter Identification in SPMSM Drive Achieved via Signal Injection

The mechanical parameters, including the Coulomb and viscous friction coefficients together with the moment of inertia, are of great interest for the performance optimization and condition evaluation of surface-mounted permanent magnet synchronous motor (SPMSM) drives. This article contributes a speed-controller-independent mechanical parameter identification scheme using open-loop speed response due to signal injection, which has not been reported in existing works. It is designed based on the premise that the viscous friction torque is disproportional to the rotor speed, which is a new progress toward estimating the mechanical parameters with high precision. Moreover, as a practical full-participation-type solution, this scheme involves a new electrical parameter estimation technique based on differential algebra to assist in identifying the mechanical parameters. This auxiliary technique attains the current-controller-free estimation of the electrical parameters with the inverter nonlinearity eliminated, thereby addressing the current controller self-commissioning and serving to acquire the accurate electromagnetic torque. The experimental evaluations on two prototype SPMSM drive systems validate the feasibility of this suggested scheme.