Estimation Of Model Parameters Research Articles

Network-based uncertainty quantification for mathematical models in epidemiology

After the new Coronavirus disease (COVID-19) emerged in the end of January 2020 in Germany, a large number of individuals suffered from severe symptoms and eventually needed intensive care in hospitals. Due to the rapid spread of the disease, the number of deceased individuals increased as well, which is a motivation to prevent as many new infections as possible. Therefore, the knowledge about the current evolution of the virus spread is crucial to predict its future behavior and to react with suitable interventions. In this paper, the evolution of the COVID-19 pandemic in Germany is forecasted by a network-based inference method, in which the interactions of individuals are taken into account using a contact matrix. Then the results are compared to the predictions without considering a contact matrix as well as to the logistic regression, which shows the advantage of incorporating the contact matrix. Furthermore, the basic reproduction number of the pandemic in Germany using a neural network approach is estimated and used for further predictions of the evolution of COVID-19 in Germany. In order to mathematically model the different compartments of the population in the considered regions, the classical SIR model is employed. In this work, we deploy the LASSO (Least Absolute Shrinkage and Selection Operator) for the unknown parameter estimation. Furthermore, we calculate and illustrate the MAPE (Mean Absolute Percentage Error) of the estimations to show the accuracy of the predictions. The results include model parameter estimation and model validation, as well as the outbreak forecasting using network-informed algorithms. Our findings show that the network-inference based approach outperforms the logistic regression as well as the neural network approach and the SIR model calibration without a contact network. Furthermore according to the results, the network-inference based approach is particularly suitable for short- to mid-term predictions, even when there is not much information about the new disease. Moreover, the predictions based on the estimation of the reproduction number in Germany can yield more reliable results with increasing the availability of data, but could not outperform the network-inference based algorithm.

A weighted Gompertz-G family of distributions for reliability and lifetime data analysis

This article is set to push new boundaries with leading-edge innovations in statistical distribution for generating up-to-the-minute contemporary distributions by a mixture of the second record value of the Gompertz distribution and the classical Gompertz model (weighted Gompertz model) using T-X characterization, especially used for two-sided schemes that provide an accurate model. The quantile, ordinary, and complete moments, order statistics, probability, and moments generating functions, entropies, probability weighted moments, Lin’s condition random variable, reliability in multicomponent stress strength system, reversed, and moments of residuals life and other reliability characteristics in engineering, actuarial, economics, and environmental technology were derived in their closed form. To investigate and test the flexibility, viability, tractability, and performance of the proposed Weighted Gompertz-G (WGG) generated model, the shapes of some sub-models of the WGG model were examined. The shapes of the sub-models indicated J-shapes, increasing, decreasing, and bathtub hazard rate functions. The maximum likelihood estimation of the WGG-generated model parameters was examined. An illustration with simulation and real-life data analysis indicated that the WGG-generated model provides consistently better goodness-of-fit statistics than some competitive models in the literature.

Development of a Predictive Statistical Pharmacological Model for Local Anesthetic Agent Effects with Bayesian Hierarchical Model Parameter Estimation.

As an alternative to animal use, computer simulations are useful for predicting pharmacokinetics and cardiovascular activities. For this purpose, we constructed a statistical model to simulate the effects of local anesthetic agents. To train the model, animal experiments were performed on 6-week-old male Hartley guinea pigs. Firstly, the guinea pigs' backs were shaved, then local anesthetic agents were subcutaneously injected, with subsequent stimulation of the anesthetized site with a needle six times at regular intervals. The number of reactions (score value) was counted. In this statistical model, the probability of reacting to needle stimulation was calculated using the elapsed time, type of local anesthetic agent, and presence or absence of adrenaline. Score values were assumed to follow a binomial distribution at the calculated probability. Parameters were estimated using the Bayesian hierarchical model and Hamiltonian Monte Carlo method. The predicted curves using the estimated parameters fitted well the observed animal values. When score values were predicted using randomly generated parameters, the median of duration was similar between animal experiments and simulations (Procaine: 55 min vs. 50 min, Lidocaine: both 60 min, and Mepivacaine: both 85 min). This approach effectively modeled the effects of local anesthetic agents. It is possible to create the simulator using the parameter values estimated in this study.

Parameter identification of transformer lumped element network model through genetic algorithm‐based gray‐box modelling technique

AbstractThe lumped element network model has been proven to be an efficient tool for the interpretation of transformer Frequency Response Analysis. However, it is challenging to obtain parameters of the model if transformer design information is unavailable. In such a case, optimisation algorithms can be used for gray‐box model parameter estimation. A methodology is developed by the authors to establish a transformer network model without winding design data, and instead, end‐to‐end open circuit Frequency Response and other terminal test results are utilised; and Genetic Algorithm is applied to approximate the unknown parameters of the model. The modelling approach developed is independent of the unit number of the network model and therefore guarantees the accuracy of optimisation. Furthermore, it can deal with transformers with a complicated winding structure such as interleaved disc type winding. Two single windings, helical and interleaved disc type, and a single‐phase 144/13 kV 60 MVA transformer are used to demonstrate the method. FRA spectra produced by the best estimated gray‐box model and the corresponding white‐box model are compared. The main features in amplitude and phase spectra are well matched, with low values of Relative Standard Deviation, for both single windings and transformer. Estimated electrical parameters show a high consistency with reference values, which are calculated based on winding design data. This validates the methodology and gives confidence to apply grey‐box modelling for FRA interpretation.

The Data Assimilation Approach in a Multilayered Uncertainty Space

The simultaneous consideration of a numerical model and of different observations can be achieved using data-assimilation methods. In this contribution, the ensemble Kalman filter (EnKF) is applied to obtain the system-state development and also an estimation of unknown model parameters. An extension of the Kalman filter used is presented for the case of uncertain model parameters, which should not or cannot be estimated due to a lack of necessary measurements. It is shown that incorrectly assumed probability density functions for present uncertainties adversely affect the model parameter to be estimated. Therefore, the problem is embedded in a multilayered uncertainty space consisting of the stochastic space, the interval space, and the fuzzy space. Then, we propose classifying all present uncertainties into aleatory and epistemic ones. Aleatorically uncertain parameters can be used directly within the EnKF without an increase in computational costs and without the necessity of additional methods for the output evaluation. Epistemically uncertain parameters cannot be integrated into the classical EnKF procedure, so a multilayered uncertainty space is defined, leading to inevitable higher computational costs. Various possibilities for uncertainty quantification based on probability and possibility theory are shown, and the influence on the results is analyzed in an academic example. Here, uncertainties in the initial conditions are of less importance compared to uncertainties in system parameters that continuously influence the system state and the model parameter estimation. Finally, the proposed extension using a multilayered uncertainty space is applied on a multi-degree-of-freedom (MDOF) laboratory structure: a beam made of stainless steel with synthetic data or real measured data of vertical accelerations. Young’s modulus as a model parameter can be estimated in a reasonable range, independently of the measurement data generation.

Estimating item parameters in multistage designs with the tmt package in R

Various likelihood-based methods are available for the parameter estimation of item response theory models (IRT), leading to comparable parameter estimates. Considering multistage testing (MST) designs, Glas (1988; https://doi.org/10.2307/1164950) stated that the conditional maximum likelihood (CML) method in its original formulation leads to severely biased parameter estimates. A modified CML estimation method for MST designs proposed by Zwitser and Maris (2015; https://doi.org/10.1007/s11336-013-9369-6) finally provides asymptotically unbiased item parameter estimates. Steinfeld and Robitzsch (2021b; https://doi.org/10.31234/osf.io/ew27f) complemented this method to MST designs with probabilistic routing strategies. For both proposed modifications additional software solutions are required since design-specific information must be incorporated into the estimation process. An R package that has implemented both modifications is "tmt". In this article, first, the proposed solutions of the CML estimation in MST designs are illustrated, followed by the main part, the demonstration of the CML item parameter estimation with the R package "tmt". The demonstration includes the process of model specification, data simulation, and item parameter estimation, considering two different routing types of deterministic and probabilistic MST designs.

American knock-out options based on floating interest rate in uncertain financial market

The knock-out options are considered as path-dependent barrier options that only expire worthless once the value of the underlying asset reaches a specific threshold. The uncertain differential equations are typically used to describe stock fluctuations in uncertain financial markets. In this study, we build a stock model considering floating interest rate based on uncertainty theory. On this basis, we mainly study the pricing scheme of American call and put options. Based on this model, we mainly research the pricing schemes for call and put options with the American barrier option. Moreover, we develope the parameter estimation for the uncertain stock model and analyze the results of the uncertain hypothesis test. Finally, we design numerical algorithms for the corresponding option pricing formulas. As an application, we verify the validity of the formulas through numerical experiments.

Indirect inference approach for parameter estimation of non linear manoeuvring models of a ROV based on model basin trials

ABSTRACT In this work, indirect inference (II) techniques are applied to estimate the parameters of a non-linear manoeuvring model of a remotely operated vehicle (ROV). In the application of this method, a set of auxiliary statistics is established in the optimisation process in order to improve the efficiency of the estimated parameters. For the parameter estimation, data from different tests are available, which were carried out with a ROV in the facilities of the Centro de Experiencias Hidrodinámicas del Pardo INTA/CEHIPAR, Madrid. The model obtained is validated by means of graphical and statistical methods with the acquired data and the statistical properties of the estimated parameters are evaluated by means of a Monte Carlo study.

Inversion of the Seepage Parameters of Earth/Rockfill Dams Considering the Coupling Effect of Seepage and Thermal Transfer

The estimation of inversion parameters for seepage models is very important for ensuring the safety of earth/rockfill dams. In most existing studies, only hydraulic characteristics have been determined based on seepage pressure or discharge observation information, which may result in inversion results that do not accurately characterize the true properties of dam materials. In this paper, an advanced parameter inversion method considering the coupling effect of seepage and thermal transfer is proposed. A seepage–thermal transfer coupled finite element model is established, and hydraulic head and temperature data of monitoring points are obtained through the forward simulation method. The entropy weight (EW) method is used to preprocess the hydraulic head and temperature data, and a universal kriging (UK) surrogate model is established to replace the time-consuming finite element simulations. The multi-island genetic algorithm (MIGA) is applied to find the optimal solution, thereby obtaining the inversion results. The effectiveness and accuracy of the proposed method are verified through laboratory tests involving seepage and thermal transfer monitoring of a core rockfill dam. Joint inversion based on temperature and hydraulic head observation information can result in improvement in the accuracy of the inversion results.

Offshore Wind Energy Assessment with a Clustering Approach to Mixture Model Parameter Estimation

In wind resource assessment research, mixture models are gaining importance due to the complex characteristics of wind data. The precision of parameter estimations for these models is paramount, as it directly affects the reliability of wind energy forecasts. Traditionally, the expectation–maximization (EM) algorithm has served as a primary tool for such estimations. However, challenges are often encountered with this method when handling complex probability distributions. Given these limitations, the objective of this study is to propose a new clustering algorithm, designed to transform mixture distribution models into simpler probability clusters. To validate its efficacy, a numerical experiment was conducted, and its outcomes were compared with those derived from the established EM algorithm. The results demonstrated a significant alignment between the new method and the traditional EM approach, indicating that comparable accuracy can be achieved without the need for solving complex nonlinear equations. Moreover, the new algorithm was utilized to examine the joint probabilistic structure of wind speed and air density in China’s coastal regions. Notably, the clustering algorithm demonstrated its robustness, with the root mean square error value being notably minimal and the coefficient of determination exceeding 0.9. The proposed approach is suggested as a compelling alternative for parameter estimation in mixture models, particularly when dealing with complex probability models.

Inversion of Geomagnetic Anomalies Caused by Ore Masses Using Hunger Games Search Algorithm

AbstractGeomagnetic anomaly interpretation through inversion procedures often yields useful results in determining the key details of ore masses. However, the problem is complicated due to the known ambiguous phenomena of the inversion process. Thus, details such as location, depth and shape can only be estimated using an efficient algorithm. To this end, we presented here a novel global optimization algorithm called Hunger Games Search (HGS) for the inversion of geomagnetic anomalies caused by ore masses. HGS is a well‐organized metaheuristic inspired by the hunger‐driven instincts and social behavioral decisions of animals. This is the first work in the literature to introduce this optimizer for the inversion of geophysical anomalies. We revealed the model parameter dependencies and the optimum control parameter values of the algorithm by performing some modal analyses and parameter tuning studies, respectively. The capability of HGS was demonstrated on synthetically produced geomagnetic responses and on three real anomalies obtained from some exploration fields in India and the USA. Uncertainty appraisal studies showed the solidity of the outputs of the algorithm. Moreover, some comparative studies with the fine‐tuned standard Particle Swarm Optimization, a commonly used tool for the inversion of geophysical anomalies, indicated that HGS algorithm provides better results in terms of convergence characteristics and solution stabilities in the presented inverse problem. We therefore recommend the use of this metaheuristic in model parameter estimation studies when dealing with this kind of geophysical potential field problems.

Analysis of Fuzzy Semantic Translation in English Language and Literature Based on Bayesian Nonparametric Model

Abstract The development of machine learning provides a new path for translating fuzzy semantics into English and literature. In this paper, we propose translation points for fuzzy semantics based on the fuzziness of language by studying the linguistic features in English literature. The hierarchical PY process under the Bayesian nonparametric model is adopted to achieve word alignment in English translation, and the clustering process of English words is controlled by introducing discount and intensity parameters. Based on this, the parameter estimation of the word probability model is completed using Gibbs sampling, and the Moses decoder extracts the translation features. Based on monolingual word classification, this model reduces 6.85% in the average time consumed per sentence compared to the Beam algorithm and 9.57% compared to the A* algorithm.

Target Reserve and Turnover Parameters Determine Rightward Shift of Enalaprilat Potency From its Binding Affinity to the Angiotensin Converting Enzyme

Drug effects are often assumed to be directly proportional to the fraction of occupied targets. However, for a number of antagonists that exhibit target-mediated drug disposition (TMDD), such as angiotensin-converting enzyme (ACE) inhibitors, drug binding to the target at low concentrations may be significant enough to influence pharmacokinetics but insufficient to elicit a drug response (i.e., differences in drug-target binding affinity and potency). In this study, a pharmacokinetic/pharmacodynamic model for enalaprilat was developed in humans to provide a theoretical framework for assessing the relationship between ex vivo drug potency (IC50) and in vivo target-binding affinity (KD). The model includes competitive binding of angiotensin I and enalaprilat to ACE and accounts for the circulating target pool. Data were obtained from the literature, and model fitting and parameter estimation were conducted using maximum likelihood in ADAPT5. The model adequately characterized time-courses of enalaprilat concentrations and four biomarkers in the renin-angiotensin system and provided estimates for in vivo KD (0.646 nM) and system-specific parameters, such as total target density (32.0 nM) and fraction of circulating target (19.8%), which were in agreement with previous reports. Model simulations were used to predict the concentration-effect curve of enalaprilat, revealing a 6.3-fold increase in IC50 from KD. Additional simulations demonstrated that target reserve and degradation parameters are key factors determining the extent of shift of enalaprilat ex vivo potency from its in vivo binding affinity. This may be a common phenomenon for drugs exhibiting TMDD and has implications for translating binding affinity to potency in drug development.

Recursive Parameter Estimation and Its Convergence for Multivariate Normal Hidden Markov Inhomogeneous Models

In this paper, will discussed parameter estimation and convergence analysis of multivariate normal hidden inhomogeneous Markov models. The results of this research show that by using the expectation maximization algorithm, a sequence of parameter estimators converges to a stationary point of the likelihood function in a monotonically increasing manner.

Statistical and dynamic model of surface morphology evolution during polishing in additive manufacturing

Many industrial components, especially those realized through 3D printing undergo surface finishing processes, predominantly, in the form of mechanical polishing. The polishing processes for custom components remain manual and iterative. Determination of the polishing endpoints, i.e., when to stop the process to achieve a desired surface finish, remains a major obstacle to process automation and in the cost-effective custom/3D printing process chains. With the motivation to automate the polishing process of 3D printed materials to a desired level of surface smoothness, we propose a dynamic model of surface morphology evolution of 3D printed materials during a polishing process. The dynamic model can account for both material removal and redistribution during the polishing process. In addition, the model accounts for increased material flow due to heat generated during the polishing process. We also provide an initial random surface model that matches the initial surface statistics. We propose an optimization problem for model parameter estimation based on empirical data using KL-divergence and surface roughness as two metrics of the objective. We validate the proposed model using data from polishing of a 3D printed sample. The procedures developed makes the model applicable to other 3D printed materials and polishing processes. We obtain a network formation model as a representation of the surface evolution from the heights and radii of asperities. We use the network connectivity (Fiedler number) as a metric for surface smoothness that can be used to determine whether a desired level of smoothness is reached or not.

Parameter estimation in nonlinear mixed effect models based on ordinary differential equations: an optimal control approach

Parameter estimation in nonlinear mixed effect models based on ordinary differential equations: an optimal control approach

Tensor-Based Temporal Control for Partially Observed High-Dimensional Streaming Data

In advanced manufacturing processes, high-dimensional (HD) streaming data (e.g., sequential images or videos) are commonly used to provide online measurements of product quality. Although there exist numerous research studies for monitoring and anomaly detection using HD streaming data, little research is conducted on feedback control based on HD streaming data to improve product quality, especially in the presence of incomplete responses. To address this challenge, this article proposes a novel tensor-based automatic control method for partially observed HD streaming data, which consists of two stages: offline modeling and online control. In the offline modeling stage, we propose a one-step approach integrating parameter estimation of the system model with missing value imputation for the response data. This approach (i) improves the accuracy of parameter estimation, and (ii) maintains a stable and superior imputation performance in a wider range of the rank or missing ratio for the data to be completed, compared to the existing data completion methods. In the online control stage, for each incoming sample, missing observations are imputed by balancing its low-rank information and the one-step-ahead prediction result based on the control action from the last time step. Then, the optimal control action is computed by minimizing a quadratic loss function on the sum of squared deviations from the target. Furthermore, we conduct two sets of simulations and one case study on semiconductor manufacturing to validate the superiority of the proposed framework.

Estimation of model parameters and simulation of earthquake ground motion by stochastic finite-fault modelling based on a modified slip-related corner frequency

Estimation of model parameters and simulation of earthquake ground motion by stochastic finite-fault modelling based on a modified slip-related corner frequency

A Solar PV Model Parameter Estimation Based on the Enhanced Self-Organization Maps

Solar photovoltaic (PV) is a commonly utilized renewable energy source, with PV cells often being modeled as electric circuits. The identification of suitable circuit model parameters for PV cells is vital for performance evaluation, efficiency calculations, and the implementation of maximum power point tracking in solar PV systems. However, modeling the solar PV system is a nonlinear problem that requires an efficient algorithm. In this paper, we employ the enhanced self-organization maps (EASOM) to efficiently reduce the search space for parameter estimation in solar PV models. Our algorithm trains the SOM network on a subset of solutions, identifies the top solution's neural unit, generates a population of potential solutions, and selects the best candidate using a cost function, which represents the best PV model parameters obtained. The performance of EASOM is verified by extracting the parameters of the single diode (SDM) and double diode (DDM) models for the STM6-40/36 PV module. EASOM outperformed state-of-the-art algorithms with the lowest RMSE and MSE values of 8.3 mA and 6.87e-05 and achieved the lowest maximum error values of 27.37 mA and 20.52 mA, as well as low power error of 66.04 mW and 62.8 mW for SDM and DDM models.

Multi-strategy adaptive guidance differential evolution algorithm using fitness-distance balance and opposition-based learning for constrained global optimization of photovoltaic cells and modules

It is of great significance to obtain the parameters of photovoltaic (PV) models quickly and accurately for the efficient operation and maintenance of PV power plants. A multi-strategy adaptive guidance differential evolution (AGDE) algorithm using fitness-distance balance (FDB) and opposition-based learning (OBL) is proposed for constrained global optimization of PV cells and modules. FDB and OBL are added on the basis of AGDE to improve the local search ability of the algorithm, and thus identify the parameters of the PV models faster and more accurately. Among the two improved strategies, FDB is a recently developed powerful method that can efficiently model selection processes in nature. In this study, the mutation mating pool of the AGDE algorithm is redesigned using the FDB method. OBL is adopted to increases the initial population diversity of AGDE. In order to verify the performance of the proposed FDB-AGDE in the parameter estimation for PV models, the experimental verification is carried out on two PV cells and three PV modules. The experimental results show that FDB-OADE has better accuracy and robustness in photovoltaic identification compared with other algorithms.