Parameter Estimation Research Articles

Phasor Measurement Unit-Driven Estimation of Transmission Line Parameters Using Variable Noise Model

Accurate parameters are crucial in modern energy systems to ensure the reliable operation of all components. Given the substantial volume of data in monitored systems, high-performance methods are necessary. This paper proposes a new Bayesian multi-output regressor for estimating the parameters of a three-phase transmission line. The presented approach achieves acceptable accuracy in parameter estimation using only one end of the line. The Bayesian regressor is developed using information derived from the data themselves, eliminating the need to explicitly model the system. This capability allows the method to estimate parameters while accommodating different noise models, even in the presence of systematic errors and non-Gaussian random noise. The methodology was validated on various systems, including a two-bus system, IEEE 14-bus, IEEE 39-bus, and IEEE 118-bus, under diverse conditions such as varying sample sizes, loads, and noise levels. These tests demonstrate the robustness of the proposed approach.

Analisis Investasi Dalam Negeri, Upah Minimum, dan Pengeluaran Pemerintah Terhadap Jumlah Penduduk Miskin di Provinsi Jawa Timur

The main goal in the global Sustainable Development Goals (SDGs) agreement is to end poverty. Appropriate and efficient government intervention is needed to reduce poverty. This research analyzes the influence of domestic investment, minimum wages and government spending in reducing poverty in East Java. Multiple linear regression analysis was used as parameter estimation for this research. The data used a time series period 2008-2022. The results show that there is a significant negative relationship between domestic investment and government spending on the poor people. This means that when domestic investment and government spending increase, it will reduce the poor people in East Java. However, this is different from the minimum wage which has a positive and significant relationship to the poor people. When the minimum wage increases, it has no effect on the number of poor people in East Java. So it can be concluded that the government can optimize domestic investment and government spending to end the problem of poverty in East Java.

Decoding lower-limb kinematic parameters during pedaling tasks using deep learning approaches and EEG.

Stroke is a neurological condition that usually results in the loss of voluntary control of body movements, making it difficult for individuals to perform activities of daily living (ADLs). Brain-computer interfaces (BCIs) integrated into robotic systems, such as motorized mini exercise bikes (MMEBs), have been demonstrated to be suitable for restoring gait-related functions. However, kinematic estimation of continuous motion in BCI systems based on electroencephalography (EEG) remains a challenge for the scientific community. This study proposes a comparative analysis to evaluate two artificial neural network (ANN)-based decoders to estimate three lower-limb kinematic parameters: x- and y-axis position of the ankle and knee joint angle during pedaling tasks. Long short-term memory (LSTM) was used as a recurrent neural network (RNN), which reached Pearson correlation coefficient (PCC) scores close to 0.58 by reconstructing kinematic parameters from the EEG features on the delta band using a time window of 250ms. These estimates were evaluated through kinematic variance analysis, where our proposed algorithm showed promising results for identifying pedaling and rest periods, which could increase the usability of classification tasks. Additionally, negative linear correlations were found between pedaling speed and decoder performance, thereby indicating that kinematic parameters between slower speeds may be easier to estimate. The results allow concluding that the use of deep learning (DL)-based methods is feasible for the estimation of lower-limb kinematic parameters during pedaling tasks using EEG signals. This study opens new possibilities for implementing controllers most robust for MMEBs and BCIs based on continuous decoding, which may allow for maximizing the degrees of freedom and personalized rehabilitation.

Point and interval estimation based on joint progressive censoring data from two Rayleigh-Weibull distribution with applications

The exploration of progressively censored data has garnered considerable attention in recent years. This research delves into the joint progressive censoring scheme applied to two populations. It presupposes that the lifespan distribution of items from these populations follows Rayleigh-Weibull distributions, characterized by varying shape and scale parameters. Within the framework of the joint progressive censoring scheme, we investigate maximum likelihood estimators for unknown parameters wherever applicable. Bayesian inferences for these parameters are presented using a Gamma prior. It’s worth noting that deriving Bayes estimators and their associated credible intervals is not feasible, hence we suggest employing the importance sampling technique for computation. To illustrate the methodologies, we analyze real-life data for demonstrative purposes, and Monte Carlo simulations are carried out to compare the performances of all the proposed methods.

Simulation-based inference on virtual brain models of disorders

Connectome-based models, also known as virtual brain models (VBMs), have been well established in network neuroscience to investigate pathophysiological causes underlying a large range of brain diseases. The integration of an individual’s brain imaging data in VBMs has improved patient-specific predictivity, although Bayesian estimation of spatially distributed parameters remains challenging even with state-of-the-art Monte Carlo sampling. VBMs imply latent nonlinear state space models driven by noise and network input, necessitating advanced probabilistic machine learning techniques for widely applicable Bayesian estimation. Here we present simulation-based inference on VBMs (SBI-VBMs), and demonstrate that training deep neural networks on both spatio-temporal and functional features allows for accurate estimation of generative parameters in brain disorders. The systematic use of brain stimulation provides an effective remedy for the non-identifiability issue in estimating the degradation limited to smaller subset of connections. By prioritizing model structure over data, we show that the hierarchical structure in SBI-VBMs renders the inference more effective, precise and biologically plausible. This approach could broadly advance precision medicine by enabling fast and reliable prediction of patient-specific brain disorders.

Physics-informed neural networks for parameter estimation and simulation of a two-group epidemiological model

This paper provides a comprehensive exploration of physics-informed neural networks and their core features. It delves into their role in tackling inverse problems inherent in ordinary differential equation-based models. Within this context, we introduce a two-group epidemiological model, elucidating its fundamental attributes. The central objective of this research is to accurately estimate the model parameters for both groups in the epidemiological model. We offer a detailed exposition of the adopted methodology, providing insights into the algorithm and the techniques employed for its implementation. Through this analysis, we illuminate the complexities of our study, contributing to the growing body of knowledge in this field, which intersects epidemiology and neural network-based parameter estimation for an enriched understanding of infectious disease dynamics.

Bootstrap-after-bootstrap for autoregressive models: an application to Indonesian value of export oil and gas

This research focuses on predicting the value of oil and gas exports in Indonesia, employing a hybrid methodology that combines autoregressive models and a bootstrap approach. Specifically, this research applies the bootstrap-after-bootstrap approach to showcase its effectiveness in improving the accuracy of parameter estimates. Analysis results indicate that the autoregressive model with an order of p=2 minimizes the AIC, BIC, and HQ values, yielding AIC=9.833775, BIC=10.03125, and HQ=9.883440, respectively. Consequently, the AR(2) model emerges as the optimal choice for predicting Indonesia's export value of oil and gas. This research utilizes varying numbers of bootstrap replications (B=100, 250, 500, 1000, and 10000) to assess the impact on prediction intervals. Prediction intervals exhibit less smoothness for B=100 and B=250, whereas B=500 and B=1000 result in a considerably smoother pattern. The highest level of smoothness is achieved for B=10000. The findings underscore that bootstrap-after-bootstrap prediction intervals provide the most accurate and conservative assessment of future uncertainty. Moreover, predictive analysis for the upcoming five periods indicates a projected decline in the export value of oil and gas in Indonesia. Overall, this research demonstrates the efficacy of the bootstrap-after-bootstrap approach in enhancing the precision of predictions and providing robust insights into future uncertainties surrounding Indonesia's oil and gas export market.

An Overview of Postprocessing in Quantum Key Distribution

Quantum key distribution (QKD) technology is a frontier in the field of secure communication, leveraging the principles of quantum mechanics to offer information-theoretically secure keys. Postprocessing is an important part of a whole QKD system because it directly impacts the secure key rate and the security of the system. In particular, with the fast increase in the photon transmission frequency in a QKD system, the processing speed of postprocessing becomes an essential issue. Our study embarks on a comprehensive review of the development of postprocessing of QKD, including five subprotocols, namely, parameter estimation, sifting, information reconciliation, privacy amplification, and channel authentication. Furthermore, we emphasize the issues raised in the implementation of these subprotocols under practical scenarios, such as limited computation or storage resources and fluctuations in channel environments. Based on the composable security theory, we demonstrate how enhancements in each subprotocol influence the secure key rate and security parameters, which can provide meaningful insights for future advancements in QKD.

Dynamic regressor extension and mixing control Lyapunov functions and high-order control Barrier functions

This paper studies the safety-critical tracking control problem for unknown structured systems with bounded disturbances and high relative degree. Firstly, a dynamic regressor extension and mixing high-order control barrier function (DREM-HOCBF) is constructed with a DREM-based robust finite-time parameter identification law. Our approach directly enforces forward invariance of the system containing parameter estimates and worst-case estimation errors to ensure system safety against parameterised uncertainty. Due to DREM, this method can approach the safety set boundary and reduce the conservatism. Meanwhile, it's also applicable to higher relative degree constraints that are more common in actual systems. Then, a DREM control Lyapunov function (DREM-CLF) that leverages the same worst-case estimation errors is proposed to guarantee that the tracking errors converge exponentially. Moreover, the method's robustness against bounded disturbances is considered. Finally, the feasibility of the developed method is verified via an adaptive cruise control (ACC) problem with unknown parameters and bounded disturbances.

Achieving Occam's razor: Deep learning for optimal model reduction.

All fields of science depend on mathematical models. Occam's razor refers to the principle that good models should exclude parameters beyond those minimally required to describe the systems they represent. This is because redundancy can lead to incorrect estimates of model parameters from data, and thus inaccurate or ambiguous conclusions. Here, we show how deep learning can be powerfully leveraged to apply Occam's razor to model parameters. Our method, FixFit, uses a feedforward deep neural network with a bottleneck layer to characterize and predict the behavior of a given model from its input parameters. FixFit has three major benefits. First, it provides a metric to quantify the original model's degree of complexity. Second, it allows for the unique fitting of data. Third, it provides an unbiased way to discriminate between experimental hypotheses that add value versus those that do not. In three use cases, we demonstrate the broad applicability of this method across scientific domains. To validate the method using a known system, we apply FixFit to recover known composite parameters for the Kepler orbit model and a dynamic model of blood glucose regulation. In the latter, we demonstrate the ability to fit the latent parameters to real data. To illustrate how the method can be applied to less well-established fields, we use it to identify parameters for a multi-scale brain model and reduce the search space for viable candidate mechanisms.

Delving into the Complexity of Analogical Reasoning: A Detailed Exploration with the Generalized Multicomponent Latent Trait Model for Diagnosis.

Research on analogical reasoning has facilitated the understanding of response processes such as pattern identification and creative problem solving, emerging as an intelligence predictor. While analogical tests traditionally combine various composition rules for item generation, current statistical models like the Logistic Latent Trait Model (LLTM) and Embretson's Multicomponent Latent Trait Model for Diagnosis (MLTM-D) face limitations in handling the inherent complexity of these processes, resulting in suboptimal model fit and interpretation. The primary aim of this research was to extend Embretson's MLTM-D to encompass complex multidimensional models that allow the estimation of item parameters. Concretely, we developed a three-parameter (3PL) version of the MLTM-D that provides more informative interpretations of participant response processes. We developed the Generalized Multicomponent Latent Trait Model for Diagnosis (GMLTM-D), which is a statistical model that extends Embretson's multicomponent model to explore complex analogical theories. The GMLTM-D was compared with LLTM and MLTM-D using data from a previous study of a figural analogical reasoning test composed of 27 items based on five composition rules: figure rotation, trapezoidal rotation, reflection, segment subtraction, and point movement. Additionally, we provide an R package (GMLTM) for conducting Bayesian estimation of the models mentioned. The GMLTM-D more accurately replicated the observed data compared to the Bayesian versions of LLTM and MLTM-D, demonstrating a better model fit and superior predictive accuracy. Therefore, the GMLTM-D is a reliable model for analyzing analogical reasoning data and calibrating intelligence tests. The GMLTM-D embraces the complexity of real data and enhances the understanding of examinees' response processes.

Output-Feedback-Based Adaptive Leaderless Consensus for Heterogenous Nonlinear Multiagent Systems With Switching Topologies.

This article investigates the leaderless output consensus control problem for a class of nonlinear multiagent systems with heterogenous system orders and unmatched unknown parameters via output-feedback control. The interaction topology among the agents is undirected and jointly connected. Due to the heterogenous system orders and switching topology among the agents, the classical distributed adaptive backstepping-based control technique cannot be applied to solve the problem considered in this article. To solve this issue, a novel distributed reference system is first proposed for each agent, by using only relative outputs of the neighboring agents. Subsequently, a fully distributed reference system-based adaptive leaderless output consensus control scheme is designed via output-feedback control. A remarkable merit of the proposed control scheme lies in that precisely known nonlinear dynamics, system states, distributed parameter estimates, and the states of virtual reference system are no longer needed to be shared with neighbors. This implies that the communication burden can be effectively alleviated, and even the communication network can be replaced by some perception sensors. Finally, two illustrative examples are provided to verify the effectiveness of the proposed control scheme.

Effect of a correlated competing risk on marginal survival estimation in an accelerated failure time model

In problems with a time to event outcome, subjects may experience competing events, which censor the outcome of interest. Cox’s partial likelihood estimator treating competing events as independent censoring is commonly used to examine group differences in clinical trials but fails to adjust for omitted covariates and can bias the assessment of marginal benefit. A bivariate normal linear model generating latent data with dependent censoring is used to assess this bias. Our R-package bnc provides maximum penalized likelihood (MPL) parameter estimation using a novel EM algorithm. Using bnc, we study the properties of such MPL estimation. Simulation results for two-sample survival comparisons of time to an event of interest, with independent censoring accompanied by censoring from a correlated competing risk, are presented. Key parameters—means, hazard ratios, and correlation—are estimated. These results demonstrated that, despite ill-conditioning in models generating correlated competing risks, estimates of marginal effects are reliable. Bivariate normal models were fitted in a trial of head and neck cancer. Model fits help with clinical interpretation while also supplementing other standard methods for follow-up that are terminated by intervening risks.

Method of Equivalent Error as a Criterion of the Assessment of the Algorithms Used for Estimation of Synchrophasor Parameters Taken from the Power System.

The development of digital techniques in control engineering leads to the creation of innovative algorithms for measuring specific parameters. In the field of electric power engineering these parameters may be amplitude, phase and frequency of voltage or current occurring in the analyzed electric grid. Thus, the algorithms mentioned, applied in relation to the quoted parameters, may provide precise and reliable measurement results in the electric grid as well as ensure better grid monitoring and security. Signal analysis regarding its identification due to the type of interference is very difficult because the multitude of information obtained is very large. In order to indicate the best method for determining errors in measuring synchronous parameters of the measured current or voltage waveforms, the authors propose in this paper a new form of one error for all testing functions, which is called an equivalent error. This error is determined for each error's value defined in the applicable standards for each of selected 15 methods. The use of the equivalent error algorithm is very helpful in identifying a group of methods whose operation is satisfactory in terms of measurement accuracy for various types of disturbances (both in the steady state and in the dynamic state) that may occur in the power grid. The results are analyzed for phasor measurement unit (PMU) devices of class P (protection) and M (measurement).

Linear Logistic Scoring Equations for Latent Class and Latent Profile Models: A Simple Method for Classifying New Cases

Researchers are often interested in using latent class or latent profile parameter estimates to obtain posterior class membership probabilities for observations other than those of the original sample. In this paper, we demonstrate that these probabilities typically take on the form of linear logistic equations with coefficients which are functions of the original model parameters. In other words, the posterior class membership probabilities can be computed with a prediction formula similar to that of a multinomial logistic regression model. We derive the scoring equations for nominal, ordinal, count, and continuous indicators, as well as investigate models with missing values on class indicators, local dependencies, covariates, or multiple latent variables. In addition to the mathematical derivations of the scoring equations, we describe how either exact or approximate scoring equations can be obtained by estimating a multinomial regression model using a weighted data set.

Inference for ARMA time series with mildly varying trend

Statistical inference is studied for ARMA time series with a mildly varying smooth trend. Following properly calibrated B-spline estimation of the trend, approximates of the unobserved ARMA series are used instead to estimate ARMA parameters by maximum likelihood. The parameter estimates are shown to be oracally efficient in the sense that they are asymptotically as efficient as if the true trend function was known and removed to obtain the true ARMA series. The mildly varying trend function is estimated by Nadaraya–Watson method with asymptotically correct simultaneous confidence band (SCB). The SCB sprawls over an interval that eventually covers the half real line, instead of a bounded interval in the existing literature, with asymptotic width of the SCB dependent on ARMA coefficients. Simulation experiments corroborate the theoretical findings.

Observability of spin precession in the presence of a black-hole remnant kick

Remnants of binary black-hole mergers can gain significant recoil or kick velocities when the binaries are asymmetric. The kick is the consequence of the anisotropic emission of gravitational waves, which may leave a characteristic imprint in the observed signal. So far, only one gravitational-wave event supports a nonzero kick velocity: GW200129_065458. This signal is also the first to show evidence for spin precession. For most other gravitational-wave observations, spin orientations are poorly constrained as this would require large signal-to-noise ratios, unequal mass ratios, or inclined systems. Here we investigate whether the imprint of the kick can help to extract more information about the spins. We perform an injection and recovery study comparing binary black-hole signals with significantly different kick magnitudes, but the same spin magnitudes and spin tilts. To exclude the impact of higher signal harmonics in parameter estimation, we focus on equal-mass binaries that are oriented face-on. This is also motivated by the fact that equal-mass binaries produce the largest kicks and many observed gravitational-wave events are expected to be close to this configuration. We generate signals with henom4a, which includes mode asymmetries. These asymmetries are the main cause for the kick in precessing binaries. For comparison with an equivalent model without asymmetries, we repeat the same injections with henom. We find that signals with large kicks necessarily include large asymmetries, and these give more structure to the signal, leading to more informative measurements of the spins and mass ratio. Our results also complement previous findings that argued precession in equal-mass, face-on, or face-away binaries is nearly impossible to identify. In contrast, we find that in the presence of a remnant kick, even those signals become more informative and allow determining precession with signal-to-noise ratios observable already by current gravitational-wave detectors. Published by the American Physical Society 2024

Estimates of Genetic Parameters, Growth Curve, and Environmental Effects for Nellore Cattle in the Pantanal.

The objective was to estimate the growth curves and genetic parameters using random regression methodology for Nellore cattle raised in Pantanal, MS, Brazil (6974 calves; n = 53,233 weights), with at least four weighings per individual. The model considered direct and maternal genetic additives and maternal permanent environmental effects at random. Orthogonal Legendre polynomials of cubic order were used to fit the growth curve. Analyses of variance were performed using the GLM procedure. The model used contained the fixed effects of sex, year of birth, farm, and the covariates calf birth month (linear and quadratic) and cow age at calving (linear and quadratic). The adjusted mean weight at 120 days of age was 93.43 ± 19.78 kg, and for 205 days of age, it was 180.42 ± 26.58 kg. Animals born in the dry season had a higher average weight [kg] (219.57 vs. 211.78, 3.7% higher) and, consequently, had higher weights at 646 days of age. Estimates of direct heritabilities (h2a) ranged from 0.35 to 0.75 (high magnitudes), and maternal heritabilities (h2m) along the trajectory of low magnitudes ranged from 0.03 to 0.08, respectively. The use of random regression to evaluate beef animals allows for adjusting the growth curve and selecting the best animals to be the parents of future generations.

How the window of visibility varies around polar angle.

Contrast sensitivity, the amount of contrast required to detect or discriminate an object, depends on spatial frequency (SF): The Contrast Sensitivity Function (CSF) peaks at intermediate SFs and drops at lower and higher SFs and is the basis of computational models of visual object recognition. The CSF varies from foveal to peripheral vision, but only a couple studies have assessed changes around polar angle of the visual field. Sensitivity is generally better along the horizontal than the vertical meridian, and better at the lower vertical than the upper vertical meridian, yielding polar angle asymmetries. Here, we investigate CSF attributes at polar angle locations at both group and individual levels, using Hierarchical Bayesian Modeling. This method enables precise estimation of CSF parameters by decomposing the variability of the dataset into multiple levels and analyzing covariance across observers. At the group level, peak contrast sensitivity and corresponding spatial frequency with the highest sensitivity are higher at the horizontal than vertical meridian, and at the lower than upper vertical meridian. At an individual level, CSF attributes (e.g., maximum sensitivity, the most preferred SF) across locations are highly correlated, indicating that although the CSFs differ across locations, the CSF at one location is predictive of the CSF at another location. Within each location, the CSF attributes co-vary, indicating that CSFs across individuals vary in a consistent manner (e.g., as maximum sensitivity increases, so does the SF at which sensitivity peaks), but more so at the horizontal than the vertical meridian locations. These results show similarities and uncover some critical polar angle differences across locations and individuals, suggesting that the CSF should not be generalized across iso-eccentric locations around the visual field. Our window of visibility varies with polar angle: It is enhanced and more consistent at the horizontal meridian.

Measuring what matters to older persons for active living: part II cross-sectional validity evidence for OPAL measure across four countries.

Through interviews with 148 older persons from four countries and in four languages, the content for a 17-item measure of active living was developed. The purpose of this paper is to present further evidence of the extent to which this new measure, Older Persons Active Living (OPAL), is "fit-for-purpose" for measuring the extent of active living at one point in time. A cross-sectional study was carried out on a population aged 65 + and living independently, drawn from a participant panel, HostedinCanada, sampling people from Canada, United States, United Kingdom, and Netherlands. The survey instrument comprised the OPAL questionnaire rated on importance and frequency, sociodemographics, and information on physical and mental function. The argument-based approach to validity framed the analyses. Logistic regression, structural equation modeling, ordinary least-squares regression, and correlation were used to generate estimates for parameters underpinning validity evidence. A total of 1612 people completed the survey, 100 to 400 people across the 6 country-language strata. The proportion of people rating the items as extremely or quite important ranged from 60 to 90%, with no important differences between men and women and few differences between strata. A single-factor structure was supported. The ordinality of the response options justified an additive total score yielding a near normal distribution (mean: 33.1; SD: 11.5; range 0-51). Correlations with other measures of converging constructs were of moderate strength (~ 0.50), and differences across groups known to affect functioning and health were observed, suggesting a Miminal Important Difference (MID) of 6 out of 51. The results of this study provide evidence that the 17-item OPAL measure is fit for the purpose of estimating the extent to which older persons are living actively at one point in time.