Parameter Estimation Methodology Research Articles

Development of a methodology for prediction and calibration of parameters of DEM simulations based on machine learning

This research work aims to develop a robust methodology for the global estimation of interaction parameters based on machine learning, applicable to the discrete element method (DEM) in the study of granular materials. The specific objectives include establishing a theoretical framework that relates the interaction micro-parameters with the macro-parameters and the physical behaviour of the material; performing DEM simulations for different material parameters; developing a machine learning-based model for global parameter estimation; and consolidating the methodology for obtaining micro-parameters for a given material and behaviour. The methodology will be applied specifically to the case of dry copper ore, evaluating its limitations and the possibility of extension to materials with other characteristics. This approach does not consider direct experimental tests, but focuses on the characterisation of the relationship between the input parameters of the material and its response through simulations, validating the response and sensitivity of the model in its different stages. The methodology is expected to allow the systematic estimation of interaction properties for a DEM model, considering micro-parameter duplicities and their global selection, aspects little addressed in the literature. The final verification includes mechanisms and key questions that facilitate future modifications and improvements, allowing its application to materials of different characteristics beyond the specific case study.

Cracking the physical insight of power law models: Bridging the gap between macroscopic kinetics and surface coverages

AbstractWe propose a methodological framework to quantify the relative abundance of key surface intermediates via analysis of the macroscopic intrinsic kinetic characteristics of gas‐phase data. At the core of this approach is the development of analytical expressions, which link reaction orders and activation energies in macroscopic power law models to the fractional coverage of the non‐observable intermediates. Through the design of an advanced parameter estimation methodology, these relationships were further exploited to develop thermodynamically consistent and mechanistic‐based power law models which could capture the evolution of surface occupancy profiles along the reactor length. The developed framework was tested through in‐silico water gas shift reaction case‐studies; the results indicate the robustness of the approach and the mechanistic insight that can be gained from its application. The methodology proposed in this study could thus be of general value to assist in reaction mechanism analysis, identification of key surface intermediates, and reactor optimization.

ESTAN—A toolbox for standardized and effective global sensitivity-based estimability analysis

The development of accurate and reliable mathematical models is the cornerstone for the modeling and optimization of processes. However, most of the existing models suffer from weak prediction capabilities due to poor data information content and poor parameter estimation methodologies. Several estimability approaches have been developed and increasingly implemented to address some of these issues. However, the wider adoption of these methods is still hampered by the lack of standardized and robust methodologies. In this paper, we present a Matlab Toolbox, called ESTAN, designed and developed to make estimability analysis accessible to non-specialist users. It uses a Quasi-Monte Carlo sequence to sample the main unknown parameters within their variation spaces. Then, depending on whether the studied model is computationally cheap or expensive, sensitivity indices are calculated either using the Sobol method or Fourier Amplitude Sensitivity Test (FAST). The calculated sensitivities are finally used within an orthogonalization algorithm to rank the parameters from the most to less estimable ones and to determine the estimable and non-estimable ones based on an estimability cut-off criterion. Various case studies are used to validate the toolbox and guide the users. The first one deals with the non-dynamic Toth adsorption model, while the second one deals with a dynamic batch cooling crystallization model. The main challenge with these two case studies is to show the importance of estimability analysis in the interpolation/extrapolation of model prediction capabilities. The last case addresses a computationally expensive thermodynamic model. The results for all the case studies are found to be promising, showing how the presented toolbox simplifies the investigation of the estimability analysis.

Frequentist and Bayesian Approaches in Modeling and Prediction of Extreme Rainfall Series: A Case Study from Southern Highlands Region of Tanzania

This study focuses on modeling and predicting extreme rainfall based on data from the Southern Highlands region, the critical for rain-fed agriculture in Tanzania. Analyzing 31 years of annual maximum rainfall data spanning from 1990 to 2020, the Generalized Extreme Value (GEV) model proved to be the best for modeling extreme rainfall in all stations. Three estimation methods–L-moments, maximum likelihood estimation (MLE), and Bayesian Markov chain Monte Carlo (MCMC)–were employed to estimate GEV parameters and future return levels. The Bayesian MCMC approach demonstrated superior performance by incorporating noninformative priors to ensure that the prior information had minimal influence on the analysis, allowing the observed data to play a dominant role in shaping the posterior distribution. Furthermore, return levels for various future periods were estimated, providing guidance for flood protection measures and infrastructure design. Trend analysis using p value, Kendall’s tau, and Sen’s slope indicated no statistically significant trends in rainfall patterns, although a weak positive trend in extreme rainfall events was observed, suggesting a gradual and modest increase over time. Overall, the study contributes valuable insights into extreme rainfall patterns and underscores the importance of L-moments in identifying the best fit distribution and Bayesian MCMC methodology for accurate parameter estimation and prediction, enabling effective measures and infrastructure planning in the region.

A Data-Driven Topology and Parameter Joint Estimation Method in Non-PMU Distribution Networks

For distribution networks, topology and line parameter information is the pre-requisite of further functions such as network analysis, operation and control. To identify the topology or estimate the parameters, a lot of existing literature relies on the knowledge of feasible topologies or full-scale deployment of advanced measuring devices, such as phase measurement units (PMUs), which is unrealistic in practice. Therefore, we propose a data-driven topology and parameter joint estimation method for non-PMU distribution networks, only using historical measurement data from smart meters. First, the topology label matrix, as a unique label of the network topology and corresponding parameters, is created and calculated based on historical data. The numeric characteristics of the topology label matrix is further analyzed to extract the topology and parameter information. Subsequently, a clustering based topology identification and parameter estimation methodology is proposed as a data-driven linear regression model. To reduce the coupling during regression, a power supply path matrix is utilized to improve the accuracy. Moreover, to improve the credibility of the method, an error-correction mechanism is proposed to indicate whether the inaccurate identification exists and how to correct it. Finally, the proposed method is tested in IEEE 33-node, 123-node networks and a large-scale system. The results demonstrate that the proposed method can provide an accurate estimation of the topology and line parameters based on samples of measurement with noise and is also effective in a large-scale system.

Bayesian model selection for COVID-19 pandemic state estimation using extended Kalman filters: Case study for Saudi Arabia.

Quantifying the uncertainty in data-driven mechanistic models is fundamental in public health applications. COVID-19 is a complex disease that had a significant impact on global health and economies. Several mathematical models were used to understand the complexity of the transmission dynamics under different hypotheses to support the decision-making for disease management. This paper highlights various scenarios of a 6D epidemiological model known as SEIQRD (Susceptible-Exposed-Infected-Quarantined-Recovered-Deceased) to evaluate its effectiveness in prediction and state estimation during the spread of COVID-19 pandemic. Then we investigate the suitability of the classical 4D epidemiological model known as SIRD (Susceptible-Infected-Recovered-Deceased) in the long-term behaviour in order to make a comparison between these models. The primary aim of this paper is to establish a foundational basis for the validity and epidemiological model comparisons in long-term behaviour which may help identify the degree of model complexity that is required based on two approaches viz. the Bayesian inference employing the nested sampling algorithm and recursive state estimation utilizing the Extended Kalman Filter (EKF). Our approach acknowledges the potential imperfections and uncertainties inherent in compartmental epidemiological models. By integrating our proposed methodology, these models can consistently generate predictions closely aligned with the observed data on active cases and deaths. This framework, implemented within the EKF algorithm, offers a robust tool for addressing future, unknown pandemics. Moreover, we present a systematic methodology for time-varying parameter estimation along with uncertainty quantification using Saudi Arabia COVID-19 data and obtain the credible confidence intervals of the epidemiological nonlinear dynamical system model parameters.

On Power Chris-Jerry Distribution: Properties and Parameter Estimation Methods

In this study, we introduce the "Power Chris-Jerry" distribution, conducting a comprehensive analysis of its fundamental mathematical characteristics and an extensive exploration of various crucial aspects. These encompass investigations into its mode, quantile function, moments, coefficient of skewness, kurtosis, moment generating function, stochastic ordering, distribution of order statistics, reliability analysis, and mean past lifetime. Furthermore, we provide an in-depth assessment of four distinct parameter estimation methodologies: maximum likelihood estimation (MLE), Least Squares (LS), maximum product spacing method (MPS), and the Method of Cram`er-von-Mises (CVM). Our investigation uncovers a consistent pattern wherein the MLE, LS, and CVM approaches consistently yield underestimated parameter values. Intriguingly, we observe a consistent trend of decreasing Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and BIAS across all estimation techniques as sample sizes increase. Remarkably, our simulation results consistently favor the Maximum Product Spacing (MPS) method, highlighting its superiority in generating estimates with smaller MSE values across a broad spectrum of parameter values and sample sizes. These findings emphasize the robustness and dependability of the MPS estimator, offering valuable insights and practical guidance for both practitioners and researchers engaged in probability distribution modeling.

Performance Comparison of Meta-Heuristics Applied to Optimal Signal Design for Parameter Identification.

This paper presents a comparative study that explores the performance of various meta-heuristics employed for Optimal Signal Design, specifically focusing on estimating parameters in nonlinear systems. The study introduces the Robust Sub-Optimal Excitation Signal Generation and Optimal Parameter Estimation (rSOESGOPE) methodology, which is originally derived from the well-known Particle Swarm Optimization (PSO) algorithm. Through a real-life case study involving an Autonomous Surface Vessel (ASV) equipped with three Degrees of Freedom (DoFs) and an aerial holonomic propulsion system, the effectiveness of different meta-heuristics is thoroughly evaluated. By conducting an in-depth analysis and comparison of the obtained results from the diverse meta-heuristics, this study offers valuable insights for selecting the most suitable optimization technique for parameter estimation in nonlinear systems. Researchers and experimental tests in the field can benefit from the comprehensive examination of these techniques, aiding them in making informed decisions about the optimal approach for optimizing parameter estimation in nonlinear systems.

A Nonlinear Recession Model for Horizontal Aquifers

AbstractRecession analysis is a powerful tool for determining the hydraulic characteristics of a riparian aquifer. The basis of the method relies on two analytical solutions of the nonlinear Boussinesq equation: one applies to a uniform water table profile in a semi‐infinite aquifer while the other pertains to a hypothetical initial profile in a finite aquifer. Both solutions assume that the water depth in the adjoining stream is negligible. In the present work, a nonlinear solution of the one‐dimensional Boussinesq equation is derived using the traveling wave approximation. The solution better represents the field conditions as it pertains to a uniform water table profile in a finite aquifer that is adjoining a stream with a non‐zero water level. It allows the derivation of simple algebraic expressions for the recession of the water table, the flow rate, and the associated drainage volume. Approximations relating the discharge rate to the outflow volume were also obtained for practical implementation in the estimation of the hydraulic parameters of the aquifer. A comparison of the proposed methodology of parameter estimation with the standard method of recession analysis showed that the present approach is superior as it avoids the pitfalls associated with the classical method, especially when daily discharge values with inherent observational errors are used. Application of the recession model to real‐world cases demonstrates its effectiveness in the estimation of the catchment‐scale hydraulic conductivity and drainable porosity.

Neural Partial Differentiation for Parameter Estimation of Flexible Aircraft Dynamics

Although the parameter estimation methodologies had been successfully applied for the rigid aircraft dynamics, the aircraft with high degree of flexibility poses challenges to determine the appropriate aeroelastic models for inclusion in the parameter estimation algorithms. Application of the neural networks for the aerodynamic modeling and parameter estimation of an aeroelastic aircraft (or flexible aircraft) is addressed in this paper. A neural network with the scaled conjugate gradient learning algorithm is used for modeling lift and pitching moment coefficients. The partial differentiation of the neural network output is carried out for the estimation of equivalent parameters of an aeroelastic aircraft. It is demonstrated that a reasonable model and estimates of the equivalent parameters for the aeroelastic aircraft are possible with the neural partial differential method by using the measured motion and control variables, without any need for postulating the coupled equations of motion or initialization of the parameters to be estimated. The proposed approach reduces the large number of parameters for aeroelastic aircraft dynamics into fewer equivalent parameters, and this methodology does not require the measurements of the elastic deflections or their derivatives. The neural partial differential method is applied to the simulated flight data of an aeroelastic aircraft for the longitudinal dynamics. The performance of the neural partial differential approach is compared with the estimates obtained from the other methods like classical estimation methods, analytical computation, and values given in the literature for rigid body modeling. The performance is also validated by comparing the measured lift force and pitching moment coefficients with the neural predicted and neural reconstructed coefficients using the estimates obtained through the neural partial differential approach.

A Novel Kinetic Modeling of Enzymatic Hydrolysis of Sugarcane Bagasse Pretreated by Hydrothermal and Organosolv Processes.

Lignocellulosic biomasses have a complex and compact structure, requiring physical and/or chemical pretreatments to produce glucose before hydrolysis. Mathematical modeling of enzymatic hydrolysis highlights the interactions between cellulases and cellulose, evaluating the factors contributing to reactor scale-up and conversion rates. Furthermore, this study evaluated the influence of two pretreatments (hydrothermal and organosolv) on the kinetics of enzymatic hydrolysis of sugarcane bagasse. The kinetic parameters of the model were estimated using the Pikaia genetic algorithm with data from the experimental profiles of cellulose, cellobiose, glucose, and xylose. The model considered the phenomenon of non-productive adsorption of cellulase on lignin and inhibition of cellulase by xylose. Moreover, it included the behavior of cellulase adsorption on the substrate throughout hydrolysis and kinetic equations for obtaining xylose from xylanase-catalyzed hydrolysis of xylan. The model for both pretreatments was experimentally validated with bagasse concentration at 10% w/v. The Plackett-Burman design identified 17 kinetic parameters as significant in the behavior of process variables. In this way, the modeling and parameter estimation methodology obtained a good fit from the experimental data and a more comprehensive model.

Estimation for multivariate normal rapidly decreasing tempered stable distributions

In this paper we describe a methodology for parameter estimation of multivariate distributions defined as normal mean-variance mixture where the mixing random variable is rapidly decreasing tempered stable distributed. We address some numerical issues resulting from the use of the characteristic function for density approximation. We focus our attention on the practical implementation of numerical methods involving the use of these multivariate distributions in the field of finance and we empirical assess the proposed algorithm through an analysis on a five-dimensional series of stock index log-returns.

Comparison of on-site versus NOAA’s extreme precipitation intensity-duration-frequency estimates for six forest headwater catchments across the continental United States

Urgency of Precipitation Intensity-Duration-Frequency (IDF) estimation using the most recent data has grown significantly due to recent intense precipitation and cloud burst circumstances impacting infrastructure caused by climate change. Given the continually available digitized up-to-date, long-term, and fine resolution precipitation dataset from the United States Department of Agriculture Forest Service’s (USDAFS) Experimental Forests and Ranges (EF) rain gauge stations, it is both important and relevant to develop precipitation IDF from onsite dataset (Onsite-IDF) that incorporates the most recent time period, aiding in the design, and planning of forest road-stream crossing structures (RSCS) in headwaters to maintain resilient forest ecosystems. Here we developed Onsite-IDFs for hourly and sub-hourly duration, and 25-yr, 50-yr, and 100-yr design return intervals (RIs) from annual maxima series (AMS) of precipitation intensities (PIs) modeled by applying Generalized Extreme Value (GEV) analysis and L-moment based parameter estimation methodology at six USDAFS EFs and compared them with precipitation IDFs obtained from the National Oceanic and Atmospheric Administration Atlas 14 (NOAA-Atlas14). A regional frequency analysis (RFA) was performed for EFs where data from multiple precipitation gauges are available. NOAA’s station-based precipitation IDFs were estimated for comparison using RFA (NOAA-RFA) at one of the EFs where NOAA-Atlas14 precipitation IDFs are unavailable. Onsite-IDFs were then evaluated against the PIs from NOAA-Atlas14 and NOAA-RFA by comparing their relative differences and storm frequencies. Results show considerable relative differences between the Onsite- and NOAA-Atlas14 (or NOAA-RFA) IDFs at these EFs, some of which are strongly dependent on the storm durations and elevation of precipitation gauges, particularly in steep, forested sites of H. J. Andrews (HJA) and Coweeta Hydrological Laboratory (CHL) EFs. At the higher elevation gauge of HJA EF, NOAA-RFA based precipitation IDFs underestimate PI of 25-yr, 50-yr, and 100-yr RIs by considerable amounts for 12-h and 24-h duration storm events relative to the Onsite-IDFs. At the low-gradient Santee (SAN) EF, the PIs of 3- to 24-h storm events with 100-yr frequency (or RI) from NOAA-Atlas14 gauges are found to be equivalent to PIs of more frequent storm events (25–50-yr RI) as estimated from the onsite dataset. Our results recommend use of the Onsite-IDF estimates for the estimation of design storm peak discharge rates at the higher elevation catchments of HJA, CHL, and SAN EF locations, particularly for longer duration events, where NOAA-based precipitation IDFs underestimate the PIs relative to the Onsite-IDFs. This underscores the importance of long-term high resolution EF data for new applications including ecological restorations and indicates that planning and design teams should use as much local data as possible or account for potential PI inconsistencies or underestimations if local data are unavailable.

Investigating Empirical Mode Decomposition in the Parameter Estimation of a Three-Section Winding Model

Parameter estimation represents an important aspect of modeling electromagnetic systems, and a wide range of parameter estimation strategies has been explored in literature. Most parameter estimation methodologies make use of either time-domain or frequency-domain responses as measured from the terminals of the device under test. Very limited research has, however, been conducted into exploring the use of modal decomposition strategies on the time-domain waveforms for parameter estimation applications. In this paper, the use of Empirical Mode Decomposition for estimating the parameters of a three-section lumped parameter transformer model is explored. A novel approach is proposed to define the optimization cost function in terms of the intrinsic modes of simulated time-domain waveforms. The results are compared with results obtained using classical time-domain and frequency-domain approaches. It is shown through an impulse response test that weighting the modes obtained from the Inferred Empirical Mode Decomposition approach presented in this work offers advantages in terms of accurately representing the target model transfer function dynamics and can assist in interpreting the various dynamic modes associated with the target model.

Parameter Estimation of a Grid-Tied Inverter Using In Situ Pseudo-Random Perturbation Sources

Inverters are playing an increasingly important role in the electrical utility grid due to the proliferation of renewable energy sources. Obtaining inverter models with accurate parameters is, therefore, essential for grid studies and design. In this paper, a methodology to estimate the output impedance and parameters of a residential grid-tied inverter is proposed. The methodology is first verified through simulation. A sensitivity analysis is conducted to determine the influence of the filter and controller parameters on the output impedance of the inverter. The simulated output impedance, voltage, and current are used in a parameter estimation methodology to obtain filter and controller parameters. It is shown that up to seven parameters can be estimated accurately. The proposed methodology is further investigated through a practical experiment. Two perturbation sources, the pseudo-random binary sequence perturbation and pseudo-random impulse sequence perturbation, are used, in turn, to perturb a residential grid-tied inverter that delivers up to 1.6 kW with the aim of obtaining its output impedance. The output impedances obtained through both pseudo-random sources are compared. It is shown that a pseudo-random binary sequence perturbation source applied in series between the grid and the inverter under test allows for the best estimation of the grid-tied inverter’s output impedance. A black-box modeling approach aimed at estimating an analytical transfer function of the output impedance from experimental data is also discussed.

Multi-pass Extended Kalman Smoother with Partially-known Constraints for Estimation of Vapor Compression Cycles

State and parameter estimation methodologies have the potential to make a significant impact in the development of broad array of capabilities for widely-used vapor compression cycles, including advanced controls, performance monitoring, data-driven modeling, and deployment of digital twin technologies. However, the nonlinearity and numerical stiffness of large physics-based models of these systems pose challenges for the practical implementation of estimators that must also satisfy the physical state constraints. We present a three-pass fixed-interval smoothing method developed in the extended Kalman estimation formalism that incorporates linear inequality and partially-known nonlinear equality constraints defined in terms of unknown parameters of the system. The smoothing method is demonstrated to have high estimation accuracy during joint state and parameter estimation of the cycle model representing a realistic system that is implemented in Julia language leveraging automatic differentiation capabilities.

Refined DC and Low-Frequency Noise Characterization at Room and Cryogenic Temperatures of Vertically Stacked Silicon Nanosheet FETs

In this work, two types of gate-all-around (GAA) vertically stacked silicon nanosheet (NS) FETs are investigated, the main difference being the vertical distance between the stacked NSs. Principal electrical parameters are estimated at room and liquid nitrogen temperatures using a refined <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Y}$ </tex-math></inline-formula> -function methodology, the main advantage being that no extra iterative steps are necessary. The results are confirmed using other derivative dc parameter estimation methodologies. Low-frequency noise measurements evidence variability of the flat-band voltage noise and correlation between the noise level and the low field mobility. The dominant flicker noise mechanism is related to the correlated mobility and carrier number fluctuation mechanism with access resistance noise contribution in very strong inversion. The impact of the access resistance on the estimation of the Coulomb scattering coefficient is evidenced.

Statistical Characterization and Modeling of Radio Frequency Signal Propagation in Mobile Broadband Cellular Next Generation Wireless Networks

An accurate assessment of the spatial and temporal radio frequency channel characteristics is essential for complex signal processing and cellular network optimization. Current research has employed numerous models to figure out how much signal propagation loss occurs along the propagation paths. However, there are issues in finding the right model for a particular terrain because these models are not universally applicable. By employing the lognormal function and the Maximum Likelihood model, a hybrid probabilistic statistical distribution model was evolved. Three LTE cell site locations in Port Harcourt, Nigeria, were used to create a hybrid model that describes the functional stochastic signal propagation loss in the area. The evaluated Maximum Likelihood model accurately estimates the relevant wireless channel properties based on observed field data. The minor square regression approach and the proposed hybrid parameter estimation methodology are compared. When it comes to estimating standard deviation errors as well as the root mean square errors, the ML‐based approach consistently outperforms the least square regression model. Finally, the proposed hybrid probabilistic statistical distribution model would be useful for mobile broadband network planning in related wireless propagation conditions.

The Influence of Anthropogenic and Environmental Disturbances on Parameter Estimation of a Dengue Transmission Model.

Some deterministic models deal with environmental conditions and use parameter estimations to obtain experimental parameters, but they do not consider anthropogenic or environmental disturbances, e.g., chemical control or climatic conditions. Even more, they usually use theoretical or measured in-lab parameters without worrying about uncertainties in initial conditions, parameters, or changes in control inputs. Thus, in this study, we estimate parameters (including chemical control parameters) and confidence contours under uncertainty conditions using data from the municipality of Bello (Colombia) during 2010-2014, which includes two epidemic outbreaks. Our study shows that introducing non-periodic pulse inputs into the mathematical model allows us to: (i) perform parameter estimation by fitting real data of consecutive dengue outbreaks, (ii) highlight the importance of chemical control as a method of vector control, and (iii) reproduce the endemic behavior of dengue. We described a methodology for parameter and sub-contour box estimation under uncertainties and performed reliable simulations showing the behavior of dengue spread in different scenarios.

A meta-heuristic optimization-based method for parameter estimation of an electric arc furnace model

Throughout distribution systems, it is usual to find non-linear time-varying loads, such as electric arc furnaces (EAFs), which are widely used in the steel-making industrial sector. Due to the process of melting and refining metals, the EAFs consume large blocks of power (active and reactive power) causing significant power quality disturbances, such as harmonics and voltage fluctuations on distribution networks. Different EAF parametric models have been proposed with the purpose to predict the voltage and current waveforms and then evaluate the performance of the reactive power compensation devices. This paper proposes a novel methodology for the optimal estimation of parameters of an electric arc furnace model, which can achieve lower execution times and error rates compared to some state-of-the-art methods. The methodology was evaluated using three meta-heuristic optimization algorithms such as the particle swarm optimization (PSO) algorithm, the vortex search algorithm (VSA) and the crow search algorithm (CSA); using real and simulated data. From the results, the proposed methodology based on meta-heuristic optimization approaches worked efficiently, allowed estimating the parameters of the electric arc furnace model using a single optimization step, capture the non-sinusoidal, non-linearity and time-varying random behavior that exhibit the real electric arc furnace samples and obtained relative errors of the total harmonic distortion between the measured and estimated voltage and arc current signals around 1.23% and 0.62%, respectively.