Parameter Estimation Procedure Research Articles

Modeling of Particle Size Distributions in Industrial Poly(vinyl chloride) Suspension Polymerization Reactors

In the present paper, a mathematical model is built and implemented to describe the trajectories of mass inventories, pressures and polymer properties with emphasis on final particle size distributions of industrial scale poly(vinyl chloride) suspension polymerization reactors. The model comprises the mass balances, statistical moment balances, equilibrium relationships and population balance equations. A discretization scheme is employed to transform the integro-differential equations resulting from the population balance model into a system of differential equations. The obtained results show, for the first time, that classical breakage and coalescence kernels described in the literature can provide very good fittings of actual industrial scale data when coupled with proper parameter estimation procedures, so that the proposed model is able to represent the available operation data with good accuracy at distinct conditions. Particularly, it is also shown that the use of a top condenser for control of the reactor temperature can lead to changes of parameters that control the particle size distributions.

A queueing model of visual search

Understanding how attentional resources are deployed in visual processing is a fundamental and highly debated topic. As an alternative to theoretical models of visual search that propose sequences of separate serial or parallel stages of processing, we suggest a queueing processing structure that entails a serial transition between parallel processing stages. We develop a continuous-time queueing model for standard visual search tasks to formalize and implement this notion. Specified as a finite-time, single-line, multiserver queueing system, the model accounts for both accuracy and response time (RT) data in visual search on a distributional level. It assumes two stages of processing. Visual stimuli first go through a massively parallel preattentive stage of feature encoding. They wait if necessary and then enter a limited-capacity attentive stage serially where multiple processing channels (“servers”) integrate features of several stimuli in parallel. A core feature of our model is the serial transition from the unlimited-capacity preattentive processing stage to the limited-capacity attentive processing stage. It enables asynchronous attentive processing of multiple stimuli in parallel and is more efficient than a simple chain of two successive, strictly parallel processing stages. The model accounts for response errors by means of two underlying mechanisms, namely, imperfect processing of the servers and, in addition, incomplete search adopted by the observer to maximize search efficiency under an accuracy constraint. For statistical inference, we develop a Monte-Carlo-based parameter estimation procedure, using maximum likelihood (ML) estimation for accuracy-related parameters and minimum distance (MD) estimation for RT-related parameters. We fit the model to two large empirical data sets from two types of visual search tasks. The model captures the accuracy rates almost perfectly and the observed RT distributions quite well, indicating a high explanatory power. The number of independent parallel processing channels that explain both data sets best was five. We also perform a Monte-Carlo model uncertainty analysis and show that the model with the correct number of parallel channels is selected for more than 90% of the simulated samples.

Estimation of time-specific intervention effects on continuously distributed time-to-event outcomes by targeted maximum likelihood estimation.

This work considers targeted maximum likelihood estimation (TMLE) of treatment effects on absolute risk and survival probabilities in classical time-to-event settings characterized by right-censoring and competing risks. TMLE is a general methodology combining flexible ensemble learning and semiparametric efficiency theory in a two-step procedure for substitution estimation of causal parameters. We specialize and extend the continuous-time TMLE methods for competing risks settings, proposing a targeting algorithm that iteratively updates cause-specific hazards to solve the efficient influence curve equationfor the target parameter. As part of the work, we further detail and implement the recently proposed highly adaptive lasso estimator for continuous-time conditional hazards with L1 -penalized Poisson regression. The resulting estimation procedure benefits from relying solely on very mild nonparametric restrictions on the statistical model, thus providing a novel tool for machine-learning-based semiparametric causal inference for continuous-time time-to-event data. We apply the methods to a publicly available dataset on follicular cell lymphoma where subjects are followed over time until disease relapse or death without relapse. The data display important time-varying effects that can be captured by the highly adaptive lasso. In our simulations that are designed to imitate the data, we compare our methods to a similar approach based on random survival forests and to the discrete-timeTMLE.

Approach for Identifying Cartesian Stiffness of a 5-Degree-of-Freedom Hybrid Robot for Machining

Abstract This article presents a systematic approach for identifying the Cartesian stiffness of a 5-degree-of-freedom (DOF) hybrid robot for machining that includes a parallel mechanism and an A/C wrist. The novelty of this approach is that the elasticities of both links and joints in the parallel mechanism are integrated into the compliance (inverse of stiffness) parameters at the limb level. By identifying the compliance parameters at the limb level rather than at the joint/link level, the number of parameters to be identified is significantly reduced and the complexity of the identification problem is decreased. Based on screw theory, the Cartesian stiffness model of this hybrid robot is established first. Then, by reconstructing this stiffness model, a linear regression model suitable for estimating the compliance parameter is derived. In addition, a two-step systematic procedure for parameter estimation is introduced, including the reconstruction of the design matrix and robust ridge estimation. Finally, both computer simulations and experiments are carried out to demonstrate the validity of the proposed approach. The simulation results show that the predictive deviations of the end-effector deflections identified by ridge estimation are less than those estimated by linear least squares, confirming its greater robustness. The experimental results indicate that the developed method has potential in industrial settings.

Phase I analysis of high-dimensional processes in the presence of outliers

One of the significant challenges in monitoring the quality of products today is the high dimensionality of quality characteristics. In this paper, we address Phase I analysis of high-dimensional processes with individual observations when the available number of samples collected over time is limited. Using a new charting statistic, we propose a robust procedure for parameter estimation in Phase I. This robust procedure is efficient in parameter estimation in the presence of outliers or contamination in the data. A consistent estimator is proposed for parameter estimation and a finite sample correction coefficient is derived and evaluated through simulation. We assess the statistical performance of the proposed method in Phase I. This assessment is carried out in the absence and presence of outliers. We show that, in both cases, the proposed control chart scheme effectively detects various kinds of shifts in the process mean. Besides, we present two real-world examples to illustrate the applicability of our proposed method.

Reaction kinetics determination and uncertainty analysis for the synthesis of the cancer drug lomustine

Fast and reliable model development frameworks are required to support current trends in modernization of pharmaceutical processing, promoting the use of digital platforms to assist process design and operation. In this work, we use a parameter estimation framework built into the PharmaPy library to determine rate parameters and uncertainty regions of different mechanistic and semi-empirical kinetic expressions for the synthesis of the drug lomustine. The parameter estimation procedure was complemented by identifiability analysis, resulting in simplified reaction mechanisms. Comparison of parameters and their uncertainty in process design was demonstrated through design space analysis, showing important differences in model prediction and the extent of their corresponding design spaces. The results of this work can serve to analyze lomustine manufacturing processes that include separation and isolation steps, where parametric uncertainty is expected to propagate along the manufacturing line and impact process feasible operation, and attainment of critical quality attributes of the product.

The t-Distribution Approach to the Second-Order Multiresponse Surface Model of Paracetamol Tablets Quality Characteristics

The normal distribution approach is often used in regression analysis at the Response Surface Methodology (RSM) modeling stage. Several studies have shown that the normal distribution approach has drawbacks compared to the more robust t-distribution approach. The t-distribution approach is found to control size much more successfully in small samples compared to existing methods in the presence of moderately heavy tails. In many RSM applications, there is more than one response (multiresponse), which is usually correlated with each other (multivariate). On the other hand, the actual response surface habitually indicates the curve by the optimal value, so the second-order model is used. This paper aims to develop the second-order multiresponse surface model using a multivariate t-distribution approach. This work also provides the parameter estimation procedure and hypothesis testing for the significance of the parameter. First, the parameter estimation is performed using the Maximum Likelihood Estimation (MLE), followed by the Expectation–Maximization algorithm as an iterative method to find (local) maximum likelihood. Next, the Likelihood Ratio Test (LRT) method is used to test the parameters simultaneously. The model obtained uses this approach to determine the conditions of input variables that optimize the Paracetamol tablets’ physical quality characteristics.

A Bayesian Semi-parametric Quantile Regression Approach for Joint Modeling of Longitudinal Ordinal and Continuous Responses

Quantile regression (QR) models are one of the methods for longitudinal data analysis. When responses seemto be skew and asymmetric due to outliers and heavy-tails, QR models may work suitably. This paper developes the semi-parametric quantile regression model for analyzing longitudinal continuous and ordinal mixed responses. The latent variable model and some threshold parameters are used to perform the quantile regression model’s ordinal part. The error of the latent variable model has Asymmetric Laplace (AL) distribution. The error term’s distribution is assumed to be AL distribution to model the continuous responses. The correlations of longitudinal responses belong to the same individual and those of mixed continuous and ordinal responses are considered using a random-effects approach. The regression spline is used to approximate the non-parametric part of the model. The parameter estimation procedure is performed under aBayesian paradigm using the Gibbs sampling method. A simulation study is performed to demonstrate the proposed model’s performance where the relative biases, standard errors, and root of MSEs of estimated parameters are decreased in the semi- parametric QR joint model when the number of subjects is increased. In our application, it was found that the mother’s age and her child’s age have significant effects on reading ability, and antisocial behavior depends on the child’s gender.

A Bayesian approach for subgroup analysis.

Several penalization approaches have been developed to identify homogeneous subgroups based on a regression model with subject-specific intercepts in subgroup analysis. These methods often apply concave penalty functions to pairwise comparisons of the intercepts, such that the subjects with similar intercept values are assigned to the same group, which is very similar to the procedure of the penalization approaches for variable selection. Since the Bayesian methods are commonly used in variable selection, it is worth considering the corresponding approaches to subgroup analysis in the Bayesian framework. In this paper, a Bayesian hierarchical model with appropriate prior structures is developed for the pairwise differences of intercepts based on a regression model with subject-specific intercepts, which can automatically detect and identify homogeneous subgroups. A Gibbs sampling algorithm is also provided to select the hyperparameter and estimate the intercepts and coefficients of the covariates simultaneously, which is computationally efficient for pairwise comparisons compared to the time-consuming procedures for parameter estimation of the penalization methods (e.g., alternating direction method of multiplier) in the case of large sample sizes. The effectiveness and usefulness of the proposed Bayesian method are evaluated through simulation studies and analysis of a Cleveland Heart DiseaseDataset.

A Flexible Zero-Inflated Poisson-Gamma Model with Application to Microbiome Sequence Count Data

In microbiome studies, it is of interest to use a sample from a population of microbes, such as the gut microbiota community, to estimate the population proportion of these taxa. However, due to biases introduced in sampling and preprocessing steps, these observed taxa abundances may not reflect true taxa abundance patterns in the ecosystem. Repeated measures, including longitudinal study designs, may be potential solutions to mitigate the discrepancy between observed abundances and true underlying abundances. Yet, widely observed zero-inflation and over-dispersion issues can distort downstream statistical analyses aiming to associate taxa abundances with covariates of interest. To this end, we propose a Zero-Inflated Poisson Gamma (ZIPG) model framework to address these aforementioned challenges. From a perspective of measurement errors, we accommodate the discrepancy between observations and truths by decomposing the mean parameter in Poisson regression into a true abundance level and a multiplicative measurement of sampling variability from the microbial ecosystem. Then, we provide a flexible ZIPG model framework by connecting both the mean abundance and the variability of abundances to different covariates, and build valid statistical inference procedures for both parameter estimation and hypothesis testing. Through comprehensive simulation studies and real data applications, the proposed ZIPG method provides significant insights into distinguished differential variability and mean abundance. Supplementary materials for this article are available online.

Flood Frequency Analysis Using Mixture Distributions in Light of Prior Flood Type Classification in Norway

The fundamental assumption of flood frequency analysis is that flood samples are generated by the same flood generation mechanism (FGM). However, flood events are usually triggered by the interaction of meteorological factors and watershed properties, which results in different FMGs. To solve this problem, researchers have put forward traditional two-component mixture distributions (TCMD-T) without clearly linking each component distribution to an explicit FGM. In order to improve the physical meaning of mixture distributions in seasonal snow-covered areas, the ratio of rainfall to flood volume (referred to as rainfall–flood ratio, RF) method was used to classify distinct FGMs. Thus, the weighting coefficient of each component distribution was determined in advance in the rainfall–flood ratio based TCMD (TCMD-RF). TCMD-RF model was applied to 34 basins in Norway. The results showed that flood types can be clearly divided into rain-on-snow-induced flood, snowmelt-induced flood and rainfall-induced flood. Moreover, the design flood and associated uncertainties were also estimated. It is found that TCMD-RF model can reduce the uncertainties of design flood by 20% compared with TCMD-T. The superiority of TCMD-RF is attributed to its clear classification of FGMs, thus determining the weighting coefficients without optimization and simplifying the parameter estimation procedure of mixture distributions.

A New Insight into Reliability Data Modeling with an Exponentiated Composite Exponential-Pareto Model

It is observed that, for some of the data in engineering and medical fields, the hazard rates increase to a high peak at the beginning and quickly decrease to a low level. In the context of survival analysis, such a hazard rate is called a upside-down bathtub hazard rate. In this paper, we investigated the properties of a model named exponentiated exponential-Pareto distribution. The model was recently proposed and applied to insurance data. We demonstrated that the model has upside-down bathtub-shaped hazard rates with specific choices of parameters. The theoretical properties such as moments, survival functions, and hazard functions were derived. The parameter estimation procedures were also introduced. We then briefly discussed the goodness-of-fit tests of the model with the simulations. Finally, we applied the model to a specific time-to-event data set along with a comparison of the performances with previous existing models. When compared to previous proposed models, the exponentiated exponential-Pareto model demonstrated good performance when fitting to such data sets.

Parameter Estimation for Hot-spot Thermal Model of Power Transformers Using Unscented Kalman Filters

This paper presents a parameter estimation technique for the hot-spot thermal model of power transformers. The proposed technique is based on the unscented formulation of the Kalman filter, jointly considering the state variables and parameters of the dynamic thermal model. A two-stage estimation technique that takes advantage of different loading conditions is developed, in order to increase the number of parameters which can be identified. Simulation results are presented, which show that the observable parameters are estimated with an error of less than 3%. The parameter estimation procedure is mainly intended for factory testing, allowing the manufacturer to enhance the thermal model of power transformers and, therefore, its customers to increase the lifetime of these assets. The proposed technique could be additionally considered in field applications if the necessary temperature measurements are available.

New Parameter Identification Method for Supercapacitor Model

The paper introduces a straightforward procedure for estimating the electrical parameters of a simple, but reasonably accurate, two-branches model of a supercapacitor (SC). The equivalent electrical circuit model includes the voltage and frequency dependence on the SC’s capacitance, neglecting the self-discharge phenomenon, so it is mainly devoted to short and mid-term simulations suitable for most industrial applications. The estimation procedure of the electrical parameters starts by analysing the experimental data achieved by a common constant-current discharge test. Such data are used to build a fitting function which is compared with the analytical solution and numerical approximations for the SC’s voltage evolution. Thus, initial estimated values of the electrical parameters are obtained through simple relations and are optimised by implementing the least squares method. The procedure is validated after an easy and fast extraction of the optimal parameters of the two-branches model of an SC. Several tests involving a commercial SC have been carried out in Simulink and the results have been compared against experimental data. A good accuracy of the two-branches model in a wide range of constant-current charging/discharging cycles is reported.

Combined Dual-Prediction Based Data Fusion and Enhanced Leak Detection and Isolation Method for WSN Pipeline Monitoring System

In a Wireless Sensor Networks (WSN) based fluid pipeline leak monitoring system, numerous sensors are deployed along the pipeline networks. A great amount of measurements are continuously transmitted from the sensor nodes to their corresponding sink nodes. The energy consumed on data transmission dominates the power depletion of a WSN system. To reduce the amount of data transmission and prolong the lifetime of WSN, in this paper, a Combined Dual-Prediction based Data Fusion (CDPDF) method is proposed. Transmissions are only triggered if the measurement is substantially different from the predicted value. Furthermore, unlike existing methods which establish the predictor by merely considering the measurements from a single sensor, the proposed CDPDF learns and updates the predictor by integrating measurements from multiple neighboring sensors, hence the spatial cross-correlation is taken into account and the prediction accuracy is significantly improved. In this paper, an Enhanced Leak Detection and Isolation (EnLDI) method is also proposed in which several important parameters, such as the friction factor and the pressure wave propagation speed, can be online updated, resulting in improvement of the leak localization accuracy. Experimental case studies are conducted. By employing the proposed CDPDF and EnLDI methods in pipeline networks monitoring, the accuracy of leak isolation is significantly increased with reduced data transmission demands. Note to Practitioners—This work delivers a hybrid scheme that combines machine learning based data fusion and transmission, with model-based leak detection and isolation. The work is motivated by the problem of high energy consumption on data transmission and poor leak diagnosis accuracy in WSN based pipeline networks monitoring system. To reduce the energy consumed during frequent transmissions among sensor nodes, in this paper, a machine learning based data fusion method is proposed which can eliminate most of the redundant transmissions. Among the investigated schemes, the Extreme Learning Machine (ELM) based predictor can not only achieve satisfactory prediction accuracy but also has low computational cost, hence it can be easily implemented in most of the embedded micro-controller systems in practice. At the base station of a WSN, in the leak diagnosis phase, traditional model-based methods employ the fixed model parameters which should be adjustable in different pressure and flow conditions etc. In this paper, an online model parameter estimation procedure is introduced and incorporated in the scheme designed to estimate the leak size and location, thus, the leak localization accuracy is significantly improved. Moreover, the algorithmic procedures, mathematical expressions, evaluation process and results are also provided for practical implementation.

The Proposal of Gamma Folded-Normal Distribution

Development of new flexible distributions for modeling non-negative measurements occuring in lifetime or reliability studies is a prominent research area in Statistics. As being the most favoured positive definite form, the Gamma distribution poses a basis for such improvements. It is well known that transforming a Gamma variable with another continuous random variable (X) creates Gamma-X family of distributions. Following this principle, we here attempted to define the X variable as Folded-Normal distributed which is also positive definite so as to propose a new family of distributions. Named as Gamma Folded-Normal distribution (GFN), our proposal is a generalization of Gamma Half-Normal distribution and contains more freely estimated parameters. This study evaluates some mathematical properties of GFN distribution such as moments and illustrates the estimation procedure for unknown parameters through a simulation study. A separate simulation is also conducted to compare the performance of this new distribution with the Folded-Normal, Half-Normal and Gamma Half-Normal distributions. Besides, the practical importance of our new proposal is illustrated by analyzing a real world data set.

Reliability assessment of transformer insulating oil using accelerated life testing

To improve the reliability and reduce the maintenance cost of transformer oil, a life prediction of transformer oil is needed so that the maintenance of transformer can be performed correctly. However, it is difficult to predict the reliable lifetime of transformer oil accurately because of its unkind operating condition at different environments. To solve this problem, based on the theory of accelerated life testing (ALT), a reliability assessment method for transformer insulating oil on a normal operational conditions is proposed. An inverse power Weibull distribution model for insulating oil lifetime with voltage is built. Numerical procedure of model parameter estimation is presented, the variances of model parameters and reliability indices, which including mean lifetime, reliability, reliable lifetime at given reliability and failure rate, are derived. The feasibility and correctness of the proposed method are validated by real lifetime data of transformer insulating oil in literature. The reliability of transformer insulating oil used at normal usage conditions are predicted by the proposed method, and the point and interval estimations of reliability indices are evaluated. The results show that reliable lifetime and mean lifetime under reliability limit should be considered simultaneously in repair or replacement of transformer insulating oil.

Dynamic modeling and parameter estimation of biomethane production from microalgae co-digestion.

This work proposes a dynamic modeling procedure applied to biomethane production from microalgae residual co-digestion. A two-stage anaerobic digestion representation is selected, considering acidogenesis and methanogenesis as main reaction pathways. Based on the experimental database generated in the University of Mons Laboratories, several candidate models, assuming the presence or absence of biomass dynamics, are suggested, and parametric structural and local identifiability studies are performed. An original parameter estimation procedure is applied to a data-set partition used for model direct validation. The remaining experiment data are dedicated to cross-validation. The results point out how these dynamic models may serve as advanced monitoring software tools such as digital twins, even in the presence of incomplete process data.

Robust estimation in functional comparative calibration models via maximum Lq-likelihood

A fully parametric estimation procedure is proposed for robust estimation of the structural parameter in a functional comparative calibration model, under normality. The proposed estimator is obtained, based on maximum Lq-likelihood approach, first replacing the incidental parameters by estimators depending on the structural parameter. The estimator, called MLqE, depends on a single distortion parameter q, which controls the balance between robustness and efficiency. If q tends to 1, the maximum likelihood estimator (MLE) is obtained. The estimation procedure can be implemented easily by a simple and fast reweighting algorithm. For applying the method to practical and real-data scenarios, a data-based choice of an appropriate value of q is proposed. Consistency and asymptotic normality is established and the covariance matrix is given. The influence function is derived, to show the local robustness properties. Theoretical properties, ease of implementabiliy and empirical results on simulated and real data show the satisfactory behavior of the MLqE and its vantages over the MLE in presence of observations discordant with the assumed model.

Excitation system voltage regulator modeling with the use of fractional calculus

The article presents a new and measurement-verified approach in the modeling of a voltage regulator, which is used in the power industry and applied for the purpose of regulation of generating units. The voltage regulator extended model, proposed in this paper, involves nonlinearities and the application of fractional calculus. The addition of these features has not only significantly increased the number of parameters determining the model response, it has also established a challenge of developing a solver capable of computing the resulting complex system of fractional differential–algebraic equations (FDAE). The mathematical formulation of a single simulation of a transient process for the model has been described. The application of the Oustaloup Recursive Approximation (ORA) of the fractional derivative has been considered in order to increase the speed of the model evaluation. Generalized equations leading to an approximating system of Differential–Algebraic Equations (DAE) have been presented in detail. In order to obtain the parameters for the fractional nonlinear model, a parameter estimation procedure has been applied, which consists of implementations of several algorithms that are executed sequentially. The usefulness and drawbacks of the application of the ORA has also been discussed.