Proposed Parameter Estimation Research Articles

Nonseparable panel models with index structure and correlated random effects

. To facilitate semiparametric estimation of general discrete-choice, censored, sample selection, and other complex panel data models, we study identification and estimation of nonseparable multiple-index models in panel data with correlated random effects and a fixed number of time periods. The parameter vectors of interest are shown to be identified up to multiplicative constants and the average marginal effects are identified under the assumption that the distribution of individual effects depends on the explanatory variables only through their averages across time. Under this assumption, we propose to estimate the unknown parameters by the generalized method of moments based on the average and outer product of the difference of derivatives of the regression function. The rate of convergence and asymptotic distribution is established both for the proposed parameter estimates and the average marginal effects. We conduct Monte Carlo simulation studies to assess finite-sample performance of the proposed estimator. We also use it to model dynamic earnings of women, and using our general identification results, we find a negative effect of the number of children not only on the selection into employment as usual, but also on the average earnings.

A Comprehensive Study on Model Simplification and Parameter Estimation of Brushless Doubly Fed Standalone Generation System

Brushless doubly-fed induction generator (BDFIG) has great potential in stand-alone generation applications. Currently, lots of control strategies have been proposed based on the BDFIG d-q model with different machine parameters ignored for simplification, but the simplification influences on model accuracy have not been discussed systematically, and the application ranges are not clear. Therefore, aiming at controller design, this paper provides a comprehensive study on model simplification and parameter estimation of brushless doubly-fed stand- alone generation. Based on the intuitive DFIG-like BDFIG model and the typical electrical quantity relations widely used in stand-alone controller design, steady-state and dynamic parameter sensitivities of BDFIG are analyzed with operation condition fully considered. Based on the analysis, the universal BDFIG simplified d-q model aiming at stand-alone control is evaluated sufficiently, and the application range is clarified. The simplification of control analysis is illustrated, and a highly-targeted and simple parameter estimation method is proposed for simplified modeling and control. Finally, simulations and experiments verify the analysis accuracy of the simplified DFIG-like BDFIG model and the feasibility of the proposed parameter estimation method.

A contact parameter estimation method for multi-modal robot locomotion on deformable granular terrains

AbstractIn this paper, we consider the problem of contact parameters (slippage and sinkage) estimation for multi-modal robot locomotion on granular terrains. To describe the contact events in the same framework for robots operated at different modes (e.g., wheel, leg), we propose a unified description of contact parameters for multi-modal robots. We also provide a parameter estimation method for multi-modal robots based on CNN and DWT (discrete wavelet transformation) techniques and verify its effectiveness over different types of granular terrains. Besides motion modes, this paper also considers the influence of slope angles and the robot’s handing angles over contact parameters. Through comparison and analysis of the prediction results, our method can not only effectively predict the contact parameters of multi-modal robot locomotion on a granular medium (better than $96\%$ accuracy) but also achieves the same or better performance when compared to other (direct) contact measurement methods designed for individual motion modes, that is, single-modal robots such as quadruped robots and mars rovers. Our proposed unified contact parameter estimation method can be useful for studying the interaction mechanics between multi-modal robots and granular terrains as well as terrain classification tasks due to its superior sensitivity which is analyzed in the experiments.

Accelerated Degradation Reliability Modeling Based on Multiple Uncertainty Wiener Processes

Numerous scholars' studies usually adopt the Wiener process to establish industrial robot performance degradation models and randomize the drift coefficients to characterize the differences in individual degradation rates, but they do not take into account the influence of measurement errors on the accuracy of the models. Aiming at the above problems, combining the Wiener process and the accelerated degradation model, the accelerated degradation reliability model of industrial robots based on the multi-uncertainty Wiener process is established, and by adding the factor of measurement error, the model is able to more accurately characterize the influence of external factors on the degradation process of industrial robots. Bayesian theory, Markov chain Monte Carlo method and Bootstrap method are used to estimate the unknown parameters in the model. Finally, the accuracy of the proposed parameter estimation method and model is verified by simulating the industrial robot performance degradation data with Monte Carlo method.

Estimation and variable selection for high-dimensional spatial dynamic panel data models

Spatiotemporal modeling of networks is of great practical importance, with modern applications in epidemiology and social network analysis. Despite rapid methodological advances, how to effectively and efficiently estimate the parameters of spatial dynamic panel models remains a challenging problem. To tackle this problem, we construct consistent complex least-squares estimators by the eigendecomposition of a spatial weight matrix method originally proposed for undirected networks. We no longer require all eigenvalues and eigenvectors to be real, which is a remarkable achievement as it implies that the proposed method is now applicable to spatiotemporal data modeling of directed networks. Under mild, interpretable conditions, we show that the proposed parameter estimators are consistent and asymptotically normally distributed. We also present a complex orthogonal greedy algorithm for variable selection and rigorously investigate its convergence properties. Moreover, we incorporate fixed effects into the spatial dynamic panel models and provide a model transformation so that the proposed method can also be applied to the transformed model. Extensive simulation studies and data examples demonstrate the effectiveness of the proposed method.

PARAMETER ESTIMATION FOR NON-LINEAR MUSKINGUM FLOOD ROUTING MODEL: NATURAL INSPIRED ALGORITHM

In any watershed the surface runoff is routed through the main course of the river to estimate the flow hydrograph at the outlet of the basin. One of the most widely used flood routing model in a river course is Muskingum model. The Muskingum model has three parameters, namely; k, x, and m, which are estimated based on the known input and outflow hydrograph of the channel. The accuracy of routing depends on the preciousness in estimating the model parameters. Many research works had been reported on improvising the parameter estimation by employing various advanced computational techniques. In this paper, we introduce a bat optimization algorithm for estimating the three parameters of the Muskingum model. Bat algorithm finds the global optimum for the parameters with random fly within the domain space. The results of the proposed model have been compared with various parameter estimation techniques reported for the Muskingum flood routing model. The comparative evaluation has been done based on four performance indicators, namely; a) Root Mean Square Error (RMSE), b) Mean absolute error (MAE), c) Coefficient of Correlation (R) , and d) Nash- Sutcliffe efficiency (E). From performance indicators it is observed that the proposed parameter estimation using a bat optimization algorithm outperforms in capturing the observed flow compared to other reported techniques. Key Words: Non-linear Muskingum model, Flood routing, parameter estimation, Bat optimization

Modelling optimal control of air pollution to reduce respiratory diseases

Respiratory diseases caused by inhalation of air pollutants are affected by seasonal changes and mitigated by air pollution control, resulting in complex dynamics. In order to investigate the effects of various factors such as random noise and air pollution control on respiratory diseases, we developed deterministic and stochastic two-dimensional coupled SIS models with multiple control measures. The proposed models and parameter estimation methods, including determinations of unknown parameter values, were used to fit the Air Quality Index (AQI) data for Xi’an city in recent 10 years. The existence of the optimal solutions for the deterministic and stochastic models were analyzed theoretically and provided to compare the parameter fitting solutions with the optimal solutions, and give theoretical support for seeking a more reasonable air pollution optimization prevention and control scheme. To show this, we conducted numerical simulations of the optimal control solution and state evolution trajectories under different weight coefficient ratios and control objectives. The results show that the stochastic optimal control problem is more consistent with the practical scenario. We also formulate the optimal control problem assuming that the control variable depends on the concentration of air pollutants. The optimal control solution reflected the periodic variation of the air pollution control strategy well. A comparison of cost values for different combinations of the three control measures illustrated that air pollution reduction is the most effective control measure.

Real-Time State of Charge-Open Circuit Voltage Curve Construction for Battery State of Charge Estimation

All state of charge (SoC) estimation algorithms based on equivalent circuit models (ECMs) estimate the open circuit voltage (OCV) and convert it to the SoC using the SoC-OCV nonlinear relation. These algorithms require the identification of ECM parameters and the nonlinear SoC-OCV relation. In literature, various techniques are proposed to simultaneously identify the ECM parameters. However, the simultaneous identification of the SoC-OCV relation remains challenging. This paper presents a novel technique to construct the SoC-OCV relation, which is eventually converted to a single parameter estimation problem. The Kalman filter is implemented to estimate the SoC and the related states in batteries using the proposed parameter estimation and the SoC-OCV construction technique. In the numerical simulations, the algorithm demonstrates that it accurately estimates the battery model parameters, and the SoC estimation error remains below 2%. We also validate the proposed algorithm with a battery experiment. The experimental results show that the error in SoC estimation remains within 2.5%.

Quantitative alignment parameter estimation for analyzing X-ray photoelectron spectra.

The interpretation of X-ray photoelectron spectroscopy (XPS) data relies on measurement models that depend on several parameters, including the photoelectron attenuation length and X-ray photon flux. However, some of these parameters are not known, because they are not or cannot be measured. The unknown geometrical parameters can be lumped together in a multiplicative factor, the alignment parameter. This parameter characterizes the ability of the exciting light to interact with the sample. Unfortunately, the absolute value of the alignment parameter cannot be measured directly, in part because it depends on the measurement model. Instead, a proxy for the experimental alignment is often estimated, which is closely related to the alignment parameter. Here, a method for estimating the absolute value of the alignment parameter based on the raw XPS spectra (i.e. non-processed photoelectron counts), the geometry of the sample and the photoelectron attenuation length is presented. The proposed parameter estimation method enables the quantitative analysis of XPS spectra using a simplified measurement model. All computations can be executed within the open and free Julia language framework PROPHESY. To demonstrate feasibility, the alignment parameter estimation method is first tested on simulated data with known acquisition parameters. The method is then applied to experimental XPS data and a strong correlation between the estimated alignment parameter and the typically used alignment proxy is shown.

Parameter estimation for a bivariate beta distribution with arbitrary beta marginals and positive correlation

We discuss a bivariate beta distribution that can model arbitrary beta-distributed marginals with a positive correlation. The distribution is constructed from six independent gamma-distributed random variates. While previous work used an approximate and sometimes inaccurate method to compute the distribution’s covariance and estimate its parameters, here, we derive all product moments and the exact covariance, which can be computed numerically. Based on this analysis we present an algorithm for estimating the parameters of the distribution using moment matching. We evaluate this inference method in a simulation study and demonstrate its practical use on a data set consisting of predictions from two correlated forecasters. Furthermore, we generalize the bivariate beta distribution to a correlated Dirichlet distribution, for which the proposed parameter estimation method can be used analogously.

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

자기저항 동기 전동기에서 자속 포화 모델의 상호 포화항에 대한 매개변수 추정

This study proposes a parameter estimation method for cross saturation term of flux saturation model including cross saturation of synchronous reluctance motor(SynRM). SynRM exhibits large cross saturation and self-saturation. A flux saturation model including the cross saturation term has been proposed to represent the cross saturation. This model satisfies the reciprocity condition, which represents a nonlinear saturation phenomenon well. It also includes a self-saturation term and a cross saturation term. The self-saturation term includes an arctangent function, and the cross saturation term includes a logarithm function and a fraction function. The parameter estimation method for the self-saturation term has been developed, but the parameter estimation method for the cross saturation term has not been presented yet. In this study, considering the role of each parameter in the cross saturation term, the parameters included in the log function are first selected. Then, the remaining parameters are estimated using the linear least squares method. The proposed parameter estimation method is verified for SynRM of 1.5 kW.

Wind Energy Resource Potential Evaluation based on Statistical Distribution Models at Four Selected Locations in Amhara Region, Ethiopia

In Ethiopia, and particularly in the Amhara region, the government as well as the concerned organization would not give special attention to establishing wind energy plants. Lack of scientific research inputs about potential assessment can be one of the reasons behind it. In this paper, a wind energy potential assessment for Debel, Malawa, Enwari, and Ayba Eyesus sites in the Amhara region has been investigated. Five statistical distribution methods namely Weibull 3P, Weibull 2P, Rayleigh 2P, Normal, and Lognormal are used to fit the data to the probability density function and cumulative distribution function. The proposed parameter estimation method, to precisely predict the values of the shape parameter, scale parameter, and location parameter, was the Maximum Likelihood Estimation Method (MLE). To analyze the goodness of fit of the models, Kolmogorov, Andersen Darling, and Chi-Square have been used. The test indicated that Weibull 3P is the best fitting method, except for Ayba Eyesus, which is suited to Weibull 2P. For Debel, Malawa, Enwari, and Ayba Eyesus, the maximum annual average wind power density was found to be 74.291 W/m2, 19.183 W/m2, 68.972 W/m2, and 49.221 W/m2 correspondingly. The evaluations show that VENSYS 87 turbine model has better performance in all three sites except Enwari, where Inox Wind DF 100 is favored. With their best performance turbine, the capacity factor of the sites is determined as 14%, 7%, 12%, and 14% for Debel, Malawa, Enwari, and Ayba Eyesus respectively. Furthermore, Economical analysis by initial cost, lifetime, operation, and maintenance cost, has been carried out to estimate the cost of energy. With VENSYS 87 turbine model, the three sites' present value costs are $5,479,586, while it costs $7,306,115 in Enwari with Inox Wind DF 100 turbine. The cost of electricity per kWh is estimated to be $0.00231, $0.00455, $0.00391, and $0.00312 for Debel, Malawa, Enwari, and Ayba Eyesus respectively, and it is significantly lower than the cost from Ethiopian electric utility (EEU), which is around 0.009$/kwh. Access to electricity in Ethiopia was reported at 45% in 2019. This indicates there is a shortage of energy in the country. This kind of study can help authorities and policymakers in taking into account wind power to mitigate energy poverty in the country.

Parameter Estimation for Balance-Equal Replicated Linear Functional Relationship Model: An Application to the Wind Directional Data

A linear functional relationship model can be used to model the relationship between two circular variables when both variables are observed with errors. When the ratio of error concentration parameter is unknown, it is suggested that the replicated linear functional relationship model be used. The purpose of this paper is to present all the parameter estimates of the replicated linear functional relationship model for balance replicates and equal circular variables. Simulations studies are performed to study understand the behavior of the parameter estimators for the balance-equal replicated linear functional relationship model. The empirical results obtained suggest that the proposed parameter estimation method performs well with small bias. A simple application of the model is demonstrated by analyzing a real dataset of a wind directional data.

On the performance of some new ridge parameter estimators in the Poisson-inverse Gaussian ridge regression

The Poisson Inverse Gaussian Regression model (PIGRM) is used for modeling the count datasets to deal with the issue of over-dispersion. Generally, the maximum likelihood estimator (MLE) is used to estimate the PIGRM estimates. In the PIGRM, when the explanatory variables are correlated, the MLE does not provide efficient results. To overcome this problem, we propose a ridge estimator for the PIGRM. The matrix mean square error (MSE) and the scalar MSE properties are derived and then compared with the MLE. In the ridge estimator, ridge parameter play a significant role, so, this study also proposes different ridge parameter estimators for the PIGRM. The performance of the proposed estimator is evaluated with the help of a simulation study and a real-life application using MSE as a performance evaluation criterion. The simulation study and the real-life application results show the superiority of the proposed parameter estimators as compared to the MLE.

Flux Saturation Model Including Cross Saturation for Synchronous Reluctance Machines and Its Identification Method at Standstill

This article proposes a magnetic flux saturation model that well represents the cross saturation of synchronous reluctance machines (SynRMs) and a parameter estimation method of the proposed saturation model. Existing magnetic flux models do not satisfy the reciprocity condition or express cross saturation well. The proposed flux saturation model consists of terms for self-saturation and cross saturation, and it expresses well the nonlinear relationship between current and flux of SynRMs, as well as satisfies the reciprocity condition. The data of flux saturation are obtained at standstill using the hysteresis voltage injection method. Using the flux saturation data, the parameters of the flux saturation model are estimated. Because the proposed magnetic flux saturation model includes an arctangent function, it is not possible to estimate parameters directly using the linear least-squares method (LSM). However, the proposed parameter estimation method integrates the self-saturation model and transforms it into a polynomial to which linear LSM can be applied. In addition, parameters related to cross saturation are also estimated using linear LSM. Therefore, the proposed parameter estimation method is easy to implement and can be applied to general-purposed inverter products. The effectiveness of the proposed model and its identification method are experimentally evaluated with a 1.5-kW SynRM. Additionally, the identified model is verified with the accuracy of the maximum torque per ampere table and the performance of sensorless control of the tested motor.

Accurate parameter estimation for safety-critical systems with unmodeled dynamics

Analysis and synthesis of safety-critical autonomous systems are carried out using models which are often dynamic. Two central features of these dynamic systems are parameters and unmodeled dynamics. Much of feedback control design is parametric in nature and as such, accurate and fast estimation of the parameters in the modeled part of the dynamic system is a crucial property for designing risk-aware autonomous systems. This paper addresses the use of a spectral lines-based approach for estimating parameters of the dynamic model of an autonomous system. Existing literature has treated all unmodeled components of the dynamic system as sub-Gaussian noise and proposed parameter estimation using Gaussian noise-based exogenous signals. In contrast, we allow the unmodeled part to have deterministic unmodeled dynamics, which are almost always present in physical systems, in addition to sub-Gaussian noise. In addition, we propose a deterministic construction of the exogenous signal in order to carry out parameter estimation. We introduce a new tool kit which employs the theory of spectral lines, retains the stochastic setting, and leads to non-asymptotic bounds on the parameter estimation error. Unlike the existing stochastic approach, these bounds are tunable through an optimal choice of the spectrum of the exogenous signal leading to accurate parameter estimation. We also show that this estimation is robust to unmodeled dynamics, a property that is not assured by the existing approach. Finally, we show that under ideal conditions with no deterministic unmodeled dynamics, the proposed approach can ensure a O˜(T) Regret, matching existing literature. Experiments are provided to support all theoretical derivations, which show that the spectral lines-based approach outperforms the Gaussian noise-based method when unmodeled dynamics are present, in terms of both parameter estimation error and Regret obtained using the parameter estimates with a Linear Quadratic Regulator in feedback.

Parameter estimation for models of major rainfall induced floods in ungaged mountain basins of Colorado

Study regionRocky Mountains in Colorado including Front and San Juan ranges Study focusHydrologic modeling of ungaged mountain basins plays an important role in ensuring the safety of Colorado’s dams. Recent research has shown that infiltration-excess runoff, saturation-excess runoff, and subsurface stormflow can all contribute to streamflow generated by extreme rainfall in Colorado’s mountains, and the soil moisture accounting (SMA) method in HEC-HMS has been suggested as an appropriate approach to model these mechanisms. However, SMA requires estimation of parameters that have not been previously considered for large floods. The objective of this work is to develop methods to estimate SMA parameters for modeling the response to extreme rainfall in ungaged mountain basins of Colorado where calibration to observed discharges is not possible. New hydrological insights for the regionThe proposed parameter estimation methods are tested for five basins in the Front Range and three basins in the San Juan Range that have streamflow data available for major flood events. For these historical events, the proposed uncalibrated models produce the same streamflow generation processes as calibrated models, and the predicted peak discharges from the uncalibrated models usually have 25% errors or smaller. For design storms, the peak discharges from the uncalibrated models can differ substantially from the peak discharges from calibrated models but are conservative relative to the envelope of observed peak discharges.

Parameter estimation of lifetime distribution for the meta-action unit with uncertainty failure modes under type-I censored data

This paper presents a parameter estimation method for the lifetime distribution of the Meta-Action Unit (MAU) with uncertainty failure modes under type-I censored data. The MAU is regarded as the basic functional unit to accomplish the function of mechanical equipment, and its failure modes are classified according to the abnormal kinematic parameters in Meta-Action (MA), which are more succinct than the traditional mechanical failure modes on parts. However, there is some uncertain information about the failure data and censored data of MAU because of the technology limitations and the space accessibility constraints for monitoring the kinematic parameters of MA, which uncertainty information can impact the parameter estimates of MAU lifetime distribution. In order to avoid the impacts on the estimating accuracy of distribution parameters, the evidential likelihood function based on the belief function theory is constructed in view of the credibility level of the failure data and censored data. In addition, the Evidential Expectation Maximization (E2M) algorithm is proposed to estimate the parameters of the mixed exponential distribution of MAU lifetime under type-I censored data. Finally, an application of an Automatic Pallet Changer (APC) is used to illustrate the validity of the MAU failure modes classification. The simulations of the E2M algorithm are conducted to show that the proposed parameters estimation method can integrate uncertain information in the failure data and the censored data, and obtain more stable results than those based on the conventional Expectation-Maximization (EM).

모델기반 swing-up 제어를 위한 2단 도립진자의 구조 설계 및 계수 추정에 대한 연구

Mathematical models and parameters with high accuracy are required for the swing-up control of a double inverted pendulum. This study proposes a mechanical structure of a double inverted pendulum having excellent matching characteristics with a mathematical model. The implementation of a parameter estimation method based on nonlinear optimization, which is essential for swing-up control, is also proposed. The proposed structure of a double inverted pendulum eliminates backlash using the direct drive of a BLDC motor, minimizes the unmodeled frictional force through bearing cleaning and oiling, minimizes unnecessary load torque using the double support of a timing pulley shaft and power transmission through a coupling, and constrains the pendulum rotation to one degree-of-freedom by adopting a dual-bearing joint. In addition, both 3D printing and CNC milling are appropriately used to satisfy the requirements for each mechanical part. The swing motion of the manufactured double inverted pendulum is measured using the lab-built light-weight rapid control prototyping 02 (LW-RCP02). The proposed parameter estimation method based on nonlinear optimization is implemented to match the response trajectory of the actual double inverted pendulum with that of a Simulink model implemented as an S-function. Finally, the effectiveness of the proposed double inverted pendulum design and parameter estimation method is confirmed by showing that the mathematical model that, based on the parameters estimated using the proposed method, accurately describes the response characteristics of the double inverted pendulum.