Parameter Estimation Method Research Articles

A State Estimation of Dynamic Parameters of Electric Drive Articulated Vehicles Based on the Forgetting Factor of Unscented Kalman Filter with Singular Value Decomposition

In this paper, a state estimation method of distributed electric drive articulated vehicle dynamics parameters based on the forgetting factor unscented Kalman filter with singular value decomposition (SVD-UKF) is proposed. The 7DOF nonlinear dynamics model of a distributed electric drive articulated vehicle is established. The unscented Kalman filter algorithm is the foundation, with singular value decomposition replacing the Cholesky decomposition. A forgetting factor is introduced to dynamically adapt the observation noise covariance matrix in real time, resulting in a centralized parameter state estimator for the articulated vehicle. The proposed parameter state estimation method based on the forgetting factor SVD-UKF is simulated and compared with the unscented Kalman filter (UKF) estimation method. Key dynamic parameters are estimated, such as the lateral and longitudinal velocities and accelerations, angular velocity, articulated angle, wheel speeds, and longitudinal and lateral tire forces of both the front and rear vehicle bodies. The results show that the proposed forgetting factor SVD-UKF method outperforms the traditional UKF method. Furthermore, a prototype vehicle test is conducted to compare the estimated values of various dynamic parameters with the actual values, demonstrating minimal errors. This verifies the effectiveness of the proposed dynamic parameter estimation method for articulated vehicles.

An online estimation method of nodal inertia parameters based on steady state operation of power system

An online estimation method of nodal inertia parameters based on steady state operation of power system

Stochastic behavior of green bond premiums

This paper aims to examine the stochastic behavior of green bond premiums that can characterize the benefits of green bonds. We propose a novel affine model of green bond pricing with mean-reverting interest rates and green bond premiums and a new model parameter estimation method using conventional and green bond prices to capture the stochastic behavior. Then, the model parameter estimation results demonstrate mean-reverting stochastic behavior for conventional bond yield and green bond premium using the US and EU green bond indexes for Corporate and three corporate bond indexes for intermediate, total, and long-term periods of the Bloomberg Fixed Income Indices from November 3, 2014 to December 11, 2020. Comparative statics using simulated green bond premiums show that green bond premiums orient toward negative values in nature. Moreover, the stochastic behavior of green bond premiums demonstrates that the greenness of green bonds has a downward effect on interest rates in COVID-19 and has a mitigating impact on liquidity risk in corporate bond markets. These results confirm the benefits of green bonds. Finally, the discussions secure the validity of the green bond pricing model by conducting econometric analyses of regime switching, principal component ones, and the GARCH (1,1) model.

Quantitative analysis model of wind energy resources in adjacent area of existing wind farms

To accurately analyze the risk resource reserves in the vicinity of wind farms and optimize the application of wind energy resources, a quantitative analysis model of wind energy resources in the vicinity of existing wind farms considering the roughness index and interference characteristics is studied. Collect and preprocess the wind energy resource data in the vicinity of existing wind farms in the national meteorological-related Internet, and build a risk resource analysis index system consisting of wind energy density, roughness index and interference characteristics according to relevant national standards; The parameter estimation method of Weibull distribution is used to calculate the density index of wind energy resources and the available hours index of wind energy resources. The roughness index is determined using the Monin–Obukhov consistent theory, and the correlation coefficient and stability are used to describe the interference characteristic index. The quantitative analysis results of wind energy resources in the vicinity of existing wind farms are obtained according to the calculation results. The experimental results show that the model can accurately calculate the roughness index and interference characteristics of the study area, and obtain high-precision quantitative analysis results for wind energy resources.

Robust Lifetime Estimation with Small Sample Sized High Speed Railway ETCS Component Data

Railway maintenance and efficient operation has been an important issue for a safe rail traffic. When an unexpected malfunction occurs on various components on the train or on the railway system, it may result in unscheduled maintenance which may cause the rail traffic to stop. In this paper, we study the random failure model of some frequently malfunctioning high-speed railway equipment based on the statistical analysis of the real data of failure records in Turkey. Popular distribution functions and parameter estimation methods have been used considering that the data has a small sample size, and it may contain outliers. In this study, we showed that for the case of a few numbers of failure data, the L-moments method gives effective results when there exists no outlier and the robust-M method gives effective results when there exists an outlier or outliers.

Estimating the distribution of parameters in differential equations with repeated cross-sectional data.

Differential equations are pivotal in modeling and understanding the dynamics of various systems, as they offer insights into their future states through parameter estimation fitted to time series data. In fields such as economy, politics, and biology, the observation data points in the time series are often independently obtained (i.e., Repeated Cross-Sectional (RCS) data). RCS data showed that traditional methods for parameter estimation in differential equations, such as using mean values of RCS data over time, Gaussian Process-based trajectory generation, and Bayesian-based methods, have limitations in estimating the shape of parameter distributions, leading to a significant loss of data information. To address this issue, this study proposes a novel method called Estimation of Parameter Distribution (EPD) that provides accurate distribution of parameters without loss of data information. EPD operates in three main steps: generating synthetic time trajectories by randomly selecting observed values at each time point, estimating parameters of a differential equation that minimizes the discrepancy between these trajectories and the true solution of the equation, and selecting the parameters depending on the scale of discrepancy. We then evaluated the performance of EPD across several models, including exponential growth, logistic population models, and target cell-limited models with delayed virus production, thereby demonstrating the ability of the proposed method in capturing the shape of parameter distributions. Furthermore, we applied EPD to real-world datasets, capturing various shapes of parameter distributions over a normal distribution. These results address the heterogeneity within systems, marking a substantial progression in accurately modeling systems using RCS data. Therefore, EPD marks a significant advancement in accurately modeling systems with RCS data, realizing a deeper understanding of system dynamics and parameter variability.

A Novel Parameter Estimation Method for Pneumatic Soft Hand Control Applying Logarithmic Decrement for Pseudo‐Rigid Body Modeling

Controlling soft robots, especially soft hand grasping, is complex due to their ubiquitous deformation, prompting the use of reduced model‐based controllers to provide sufficient state information for high dynamic response control performance. However, most modeling techniques face computational efficiency and complexity of parameter identification issues. To alleviate this, a paradigm coupling an analytical modeling approach based on pseudo‐rigid body modeling and the logarithmic decrement method (PRBM + LDM) for parameter estimation is proposed. Using a soft robot hand test bed, the PRBM + LDM model for a closed‐loop position controller is applied and is compared with a simple proportional–integral–derivative controller (PID controller) static shape control of soft continuum robots using deep visual inverse kinematic models. Furthermore, the PRBM + LDM model‐based force controller is compared with simple constant pressure grasping control by pinching tasks on low‐weight, small objects—a screwdriver, a potato chip, and a brass coin. The PRBM + LDM‐based position controller outperforms the simple PID position controller, and the PRBM + LDM‐based force controller achieves a higher success rate than the constant pressure grasping control in the pinching tasks. In conclusion, the PRBM + LDM modeling technique proves to be a convenient and efficient way to model the dynamic behavior of soft actuators closely and can be applied to build high‐precision position and force controllers.

Modelling heart rate dynamics in relation to speed and power output in sprint kayaking as a basis for training evaluation and optimisation.

With the development of power output sensors in the field of paddle sports and the ongoing advancements in dynamical analysis of exercise data, this study aims to model the measurements of external training intensity in relation to heart rate (HR) time-series during flat-water kayak sprint. Nine elite athletes performed a total of 47 interval training sessions with incremental intensity (light to (sub-) maximal effort levels). The data of HR, speed and power output were measured continuously and rating of perceived exertion and blood lactate concentration ([BLa]) were sampled at the end of each interval stage. Different autoregressive-exogenous (ARX) modelling configurations are tested, and we report on which combination of input (speed or power), model order (1st or 2nd), parameter estimation method (time-(in)variant) and training conditions (ergometer or on-water) is best suited for linking external to internal measures. Average model R2 values varied between 0.60 and 0.97, with corresponding average root mean square error values of 15.6 and 3.2 bpm. 1st order models with time-varying (TV) parameter estimates yield the best model performance (average R2=0.94). At the level of the individual athlete, the TV modelling features (i.e., the model parameters and derivatives such as time constant values) show significant repeated measure correlations in relation to measures of exercise intensity. In conclusion, the study provides a comprehensive description of how the dynamic relationship between external load and HR for sprint kayaking training data can be modelled. Such models can be used as a basis for improving training evaluation and optimisation.

Advanced inference techniques for two-parameter Topp-Leone models under unified progressively hybrid censoring

In this study, we examine the unified progressive hybrid censoring scheme from Topp-Leone models, and we show that while the maximum likelihood estimates of the model parameters are uniquely exist, they cannot be obtained in a closed form. To obtain these estimates, we utilize two frequentist algorithms—the Expectation-Maximization method and an Expectation-Maximization type method. We also derive confidence intervals for the unknown parameters using both asymptotic distributions of the maximum likelihood estimators and bootstrap approaches. Furthermore, we develop sample-based Bayes estimates for the model parameters under different error loss functions, such as square, LINEX, and entropy loss functions. To approximate the Bayes estimates, we apply importance sampling and Metropolis-Hastings algorithms. We also construct Bayes credible intervals for the estimates. To assess the performance of the proposed methods, we conduct a numerical simulation study. Finally, we analyze a real data set to illustrate the practical application of our proposed methods and their findings. The study highlights the usefulness of hybrid censoring schemes and the applicability of various statistical methods for parameter estimation and inference.

Comparison between classical and Bayesian estimation with joint Jeffrey’s prior to Weibull distribution parameters in the presence of large sample conditions

Weibull distribution has been considered one of the most common and valuable distributions for building and analyzing good models for lifetime data. Many researchers have studied the properties of Weibull distribution, also in search of the best method to estimate both parameters. In this paper, we proposed a comparison of Weibull distribution parameters under large sample conditions. We chose to study the classical estimation methods of Weibull distribution parameters, including the maximum likelihood estimator and moments estimation (ME). Next, we compared these methods with the Bayesian estimation method (BE) with Jeffrey’s prior function. We validated the proposed study via simulation using both small and large samples. We used mean square errors (MSE) to determine the best estimation method. Our simulation findings suggest that maximum likelihood estimators are reasonably effective when using small sample sizes. In addition, in cases where the sample size is larger, the BE performed more effectively for both scale and shape parameters of the Weibull distribution function.

Identification and application of dynamic parameters of manipulator based on improved IRLS algorithm

Purpose To overcome the shortcomings of traditional dynamic parameter identification methods in accuracy and efficiency, this paper aims to propose a dynamic parameter identification method based on improved iterative reweighted least squares (IIRLS) algorithm. Design/methodology/approach First, Newton–Euler method is used to establish the dynamic model of the robot, which is linearized and reorganized. Then, taking the improved Fourier series as the excitation trajectory, the optimization model with objective function is established and optimized. Then, the manipulator runs the optimized trajectory and collects the running state of the joint. Finally, the iterative process of iterative reweighted least squares (IRLS) algorithm is improved by combining clustering algorithm and matrix inversion operation rules, and the dynamic model of robot is identified by using the processed collected data. Findings Experimental results show that, compared with the IRLS algorithm, the root mean square of the proposed IIRLS algorithm is reduced by 4.18% and the identification time is reduced by 94.92% when the sampling point is 1001. This shows that IIRLS algorithm can identify the dynamic model more accurately and efficiently. Originality/value It effectively solves the problem of low accuracy and efficiency of parameter identification in robot dynamic model and can be used as an effective method for parameter estimation of robot dynamic model, which is of great significance to the research of control method based on robot model.

Variational Bayesian Estimation of Quantile Nonlinear Dynamic Latent Variable Models with Possible Nonignorable Missingness

Our study presents an innovative variational Bayesian parameter estimation method for the Quantile Nonlinear Dynamic Latent Variable Model (QNDLVM), particularly when dealing with missing data and nonparametric priors. This method addresses the computational inefficiencies associated with the traditional Markov chain Monte Carlo (MCMC) approach, which struggles with large datasets and high-dimensional parameters due to its prolonged computation times, slow convergence, and substantial memory consumption. By harnessing the deterministic variational Bayesian framework, we convert the complex parameter estimation into a more manageable deterministic optimization problem. This is achieved by leveraging the hierarchical structure of the QNDLVM and the principle of efficiently optimizing approximate posterior distributions within the variational Bayesian framework. We further optimize the evidence lower bound using the coordinate ascent algorithm. To specify propensity scores for missing data manifestations and covariates, we adopt logistic and probit models, respectively, with conditionally conjugate mean field variational Bayes for logistic models. Additionally, we utilize Bayesian local influence to analyze the Ecological Momentary Assessment (EMA) dataset. Our results highlight the variational Bayesian approach’s notable accuracy and its ability to significantly alleviate computational demands, as demonstrated through simulation studies and practical applications.

Modeling of deep ocean ambient noise and sound-ray-arrival-grazing-angle estimation for shallow receivers.

The ambient noise model of isotropic fields is not applicable to shallow-located platforms in the deep ocean, and the conventional methods for estimating the sound-ray-arrival-grazing-angle of targets do not account for the effects of surface noise. Therefore, target parameter estimation methods based on a single vector hydrophone are explored in this study. The approach used in this study integrates the hydroacoustic physical model, signal processing method, and ocean ambient. A time-domain model of the vector field of deep ocean ambient noise was developed for receivers positioned at shallow depths, followed by derivation of the covariance matrix of the single vector hydrophone based on this model. Subsequently, a target signal-to-noise ratio (SNR) estimation method using the covariance matrix derived from the single vector hydrophone was formulated. This method effectively addresses the challenge of distinguishing between target signal and noise by transforming the power estimation problem into a covariance matrix solving the task. Finally, a refined approach for estimating the sound-ray-arrival-grazing-angle of target is proposed, aiming to theoretically mitigate the impact of surface noise on the target signal. The experimental data obtained from a deep ocean region in the South China Sea indicate that the findings obtained using the method proposed in this study are consistent with the reference values derived from automatic identification system information. The method also demonstrates reliable estimation results even when the SNR exceeds -5 dB. The conceptual framework developed for SNR and sound-ray-arrival-grazing-angle estimation in this study can be readily applied to other ambient models, indicating potential applications in engineering field. The primary objective of the study was to enhance and augment underwater acoustic signal processing methods for shallow receivers deployed in the deep ocean.

New Bounded Probability Model: Properties, Estimation, and Applications

The article introduces a new unit distribution, an extension of Tiessier distribution, characterized by a versatile hazard function capable of adopting diverse shapes such as bathtub or N-shaped curves. An exploration of the fundamental properties of this distribution is undertaken, accompanied by the implementation of the maximum likelihood estimation technique and eleven alternative methods to approximate its parameters effectively. Through a simulation study, the article effectively demonstrates the precision of these parameter estimation methods, even when dealing with small sample sizes. Two datasets are employed to apply the novel distribution, subjecting it to a comprehensive evaluation against established models utilizing a range of model selection criteria and goodness of fit tests. Notably, the article illustrates that the performance of the new distribution surpasses that of existing models in effectively capturing data patterns. Beyond its empirical contributions, the article highlights the potential cross-disciplinary applications of the new distribution in many fields while concurrently advancing the realms of probability theory and statistical inferences.

Nonlinear parameter estimation with physics-constrained spectral–spatial priors for highly accelerated chemical exchange saturation transfer MRI

Objective.To develop a nonlinear, model-based parameter estimation method directly from incomplete measurements ink - wspace for robust spectral analysis in highly accelerated chemical exchange saturation transfer (CEST) magnetic resonance imaging (MRI).Approach. A CEST-specific, separable nonlinear model, which describes spectral decomposition using multi-pool Lorentzian functions (conventional magnetization transfer (MT), direct saturation of water signals (DS), amide, amine, and nuclear Overhauser effect) derived from the steady-state Bloch McConnel equation, is incorporated into a measurement model in CEST MRI. Furthermore, signal drop in saturation transfer experiments is formulated by an additional, separable nonlinear spectral prior indicating that the symmetric z-spectra synthesized using conventional MT and DS always remain higher or equal to the whole z-spectra with all pools. Given the above considerations, linear and nonlinear parameters in the proposed method are estimated in an alternating fashion directly from highly incomplete measurements ink - wspace by solving a constrained optimization problem with the physics-constrained spectral priors while imposing additional sparsity priors on spatial parameter maps.Main results.Compared with conventional methods, the proposed method yields clearer delineation of tumor-specific CEST maps without apparent artifact and noise.Significance.We successfully demonstrated the feasibility of the proposed method for CEST MRI with highly incomplete measurements thus enabling high-resolution whole brain CEST MRI in clinically reasonable imaging time.

Smoothed Weighted Quantile Regression for Censored Data in Survival Analysis

In this study, we propose a smoothed weighted quantile regression (SWQR), which combines convolution smoothing with a weighted framework to address the limitations. By smoothing the non-differentiable quantile regression loss function, SWQR can improve computational efficiency and allow for more stable model estimation in complex datasets. We construct an efficient optimization process based on gradient-based algorithms by introducing weight refinement and iterative parameter estimation methods to minimize the smoothed weighted quantile regression loss function. In the simulation studies, we compare the proposed method with two existing methods, including martingale-based quantile regression (MartingaleQR) and weighted quantile regression (WeightedQR). The results emphasize the superior computational efficiency of SWQR, outperforming other methods, particularly WeightedQR, by requiring significantly less runtime, especially in settings with large sample sizes. Additionally, SWQR maintains robust performance, achieving competitive accuracy and handling the challenges of right censoring effectively, particularly at higher quantiles. We further illustrate the proposed method using a real dataset on primary biliary cirrhosis, where it exhibits stable coefficient estimates and robust performance across quantile levels with different censoring rates. These findings highlight the potential of SWQR as a flexible and robust method for analyzing censored data in survival analysis, particularly in scenarios where computational efficiency is a key concern.

A Novel Time-Varying P-III Distribution Curve Fitting Model to Estimate Design Floods in Three Gorges Reservoir Operation Period

Design floods are traditionally estimated based on the at-site annual maximum flood series, including historical information of hydraulic structures. Nevertheless, the construction and operation of upstream reservoirs undermine the assumption of stationarity in the downstream flood data series. This paper investigates non-stationary design flood estimation considering historical information from the Three Gorges Reservoir (TGR) in the Yangtze River. Based on the property that the distribution function of a continuous random variable increases monotonically, we proposed a novel time-varying P-III distribution coupled with the curve fitting method (referred to as the Tv-P3/CF model) to estimate design floods in the TGR operation period, and we comparatively studied the reservoir indices and parameter estimation methods. The results indicate that: (1) The modified reservoir index used as a covariate can effectively capture the non-stationary characteristics of the flood series; (2) The Tv-P3/CF model emphasizes the fitness of historical information, yielding superior results compared to time-varying P-III distribution estimated by the maximum likelihood method; (3) Compared to the original design values, the 1000-year design peak discharge Qm and 3-day and 7-day flood volumes in the TGR operation period are reduced by approximately 20%, while the 15-day and 30-day flood volumes are reduced by about 16%; (4) The flood-limited water level of the TGR can be raised from 145 m to 154 m, which can annually generate 0.32 billion kW h more hydropower (or increase by 6.8%) during flood season without increasing flood prevention risks.

Introducing the unit Zeghdoudi distribution as a novel statistical model for analyzing proportional data

Unit distributions are essential in statistical modeling, providing a robust framework for understanding variables constrained within the unit interval [0,1]. This interval is crucial in public health, environmental studies, engineering, and finance, where measurements often represent proportions, probabilities, or rates. Despite numerous unit distributions derived by transforming existing distributions, there remains a pressing need for new distributions that can accommodate the unique characteristics of diverse datasets. In this study, we introduce the unit Zeghdoudi distribution (UZD), a novel transformation of the Zeghdoudi distribution (ZD). This new distribution retains the simplicity of the original ZD while offering enhanced flexibility and precision in modeling data confined to the unit interval. The UZD exhibits several noteworthy features, including both right and left-skewed probability density functions, a closed-form quantile function, easily defined moments, and manageable entropies. Using sixteen classical methods for parameter estimation, supported by a comprehensive simulation study, we demonstrate the efficiency and reliability of the UZD. Finally, the application of the UZD to three real-world proportional datasets related to (COVID-19, environmental, and radiation datasets) underscores its effectiveness and demonstrates its superiority over several established models.

Deep Learning-Based Method for Detecting Traffic Flow Parameters Under Snowfall.

In recent years, advancements in computer vision have yielded new prospects for intelligent transportation applications, specifically in the realm of automated traffic flow data collection. Within this emerging trend, the ability to swiftly and accurately detect vehicles and extract traffic flow parameters from videos captured during snowfall conditions has become imperative for numerous future applications. This paper proposes a new analytical framework designed to extract traffic flow parameters from traffic flow videos recorded under snowfall conditions. The framework encompasses four distinct stages aimed at addressing the challenges posed by image degradation and the diminished accuracy of traffic flow parameter recognition caused by snowfall. The initial two stages propose a deep learning network for removing snow particles and snow streaks, resulting in an 8.6% enhancement in vehicle recognition accuracy after snow removal, specifically under moderate snow conditions. Additionally, the operation speed is significantly enhanced. Subsequently, the latter two stages encompass yolov5-based vehicle recognition and the employment of the virtual coil method for traffic flow parameter estimation. Following rigorous testing, the accuracy of traffic flow parameter estimation reaches 97.2% under moderate snow conditions.

Advancing Continuous Distribution Generation: An Exponentiated Odds Ratio Generator Approach.

This paper presents a new methodology for generating continuous statistical distributions, integrating the exponentiated odds ratio within the framework of survival analysis. This new method enhances the flexibility and adaptability of distribution models to effectively address the complexities inherent in contemporary datasets. The core of this advancement is illustrated by introducing a particular subfamily, the "Type 2 Gumbel Weibull-G family of distributions". We provide a comprehensive analysis of the mathematical properties of these distributions, including statistical properties such as density functions, moments, hazard rate and quantile functions, Rényi entropy, order statistics, and the concept of stochastic ordering. To test the robustness of our new model, we apply five distinct methods for parameter estimation. The practical applicability of the Type 2 Gumbel Weibull-G distributions is further supported through the analysis of three real-world datasets. These real-life applications illustrate the exceptional statistical precision of our distributions compared to existing models, thereby reinforcing their significant value in both theoretical and practical statistical applications.