scholarly journals A Kronecker-based Covariance Specification for Spatially Continuous Multivariate Data

2022 ◽  
Author(s):  
Angélica Maria Tortola Ribeiro ◽  
Paulo Justiniano Ribeiro ◽  
Wagner Hugo Bonat
Keyword(s):  
Spatial Data ◽  
Likelihood Function ◽  
Asymptotic Properties ◽  
Multivariate Data ◽  
Gaussian Random Fields ◽  
Computational Time ◽  
Attractive Alternative ◽  
Forecast Errors ◽  
Covariance Functions ◽  
Proposed Model

Abstract We propose a covariance specification for modeling spatially continuous multivariate data. This model is based on a reformulation of Kronecker’s product of covariance matrices for Gaussian random fields. We illustrate the case with the Matérn function used for specifying marginal covariances. The structure holds for other choices of covariance functions with parameters varying in their usual domains, which makes the estimation process more accessible. The reduced computational time and flexible generalization for increasing number of variables, make it an attractive alternative for modelling spatially continuous data. Theoretical results for the likelihood function and the derivatives of the covariance matrix are presented. The proposed model is fitted to the literature’s soil250 dataset, and adequacy measures, forecast errors and estimation times are compared with the ones obtained based on classical models. Furthermore, the model is fitted to the classic meuse dataset to illustrate the model’s flexibility in a four-variate analysis. A simulation study is performed considering different parametric scenarios to evaluate the asymptotic properties of the maximum likelihood estimators. The satisfactory results, its simpler structure and the reduced estimation time make the proposed model a candidate approach for multivariate analysis of spatial data.

Point processes on the complex plane with applications

2019 ◽  
Author(s):  
◽  
Weichao Wu
Keyword(s):  
Point Process ◽  
Complex Plane ◽  
Spatial Data ◽  
Point Processes ◽  
Dimensional Space ◽  
Gaussian Random Fields ◽  
Process Models ◽  
Covariance Functions ◽  
Complex Point ◽  
Log Linear

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] A point process is a random collection of points from a certain space, and point process models are widely used in areas dealing with spatial data. However, studies of point process theory in the past only focused on Euclidean spaces, and point processes on the complex plane have been rarely explored. In this thesis we introduce and study point processes on the complex plane. We present several important quantities of a complex point process (CPP) that investigate first and second order properties of the process. We further introduce the Poisson complex point process and model its intensity function using log-linear and mixture models in the corresponding 2-dimensional space. The methods are exemplified via applications to density approximation and time series analysis via the spectral density, as well as construction and estimation of covariance functions of Gaussian random fields.

scholarly journals Improved Modeling of a Multi-Level Inverter for TACS to Reduce Computational Time and Improve Accuracy

Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 849
Author(s):  
Sung-An Kim
Keyword(s):  
Mechanical Model ◽  
Simulation Software ◽  
Computational Time ◽  
Electrical Model ◽  
Conventional Model ◽  
Switching Operation ◽  
Air Compressor ◽  
Power Semiconductors ◽  
Proposed Model ◽  
Multi Level

A modeling of a turbo air compressor system (TACS), with a multi-level inverter for driving variable speed, combining an electrical model of an electric motor drive system (EMDS) and a mechanical model of a turbo air compressor, is essential to accurately analyze dynamics characteristics. Compared to the mechanical model, the electrical model has a short sampling time due to the high frequency switching operation of the numerous power semiconductors inside the multi-level inverter. This causes the problem of increased computational time for dynamic characteristics analysis of TACS. To solve this problem, the conventional model of the multi-level inverter has been proposed to simplify the switching operation of the power semiconductors, however it has low accuracy because it does not consider pulse width modulation (PWM) operation. Therefore, this paper proposes an improved modeling of the multi-level inverter for TACS to reduce computational time and improve the accuracy of electrical and mechanical responses. In order to verify the reduced computational time of the proposed model, the conventional model using the simplified model is compared and analyzed using an electronic circuit simulation software PSIM. Then, the improved accuracy of the proposed model is verified by comparison with the experimental results.

scholarly journals The time machine: a simulation approach for stochastic trees

2011 ◽  
Vol 467 (2132) ◽  
pp. 2350-2368 ◽  
Author(s):  
Ajay Jasra ◽  
Maria De Iorio ◽  
Marc Chadeau-Hyam
Keyword(s):  
Variance Reduction ◽  
Sequential Monte Carlo ◽  
Likelihood Function ◽  
Computing Time ◽  
Point Of View ◽  
Computational Time ◽  
Recent Common Ancestor ◽  
Theoretical Point ◽  
Monte Carlo Techniques ◽  
Most Recent Common Ancestor

In this paper, we consider a simulation technique for stochastic trees. One of the most important areas in computational genetics is the calculation and subsequent maximization of the likelihood function associated with such models. This typically consists of using importance sampling and sequential Monte Carlo techniques. The approach proceeds by simulating the tree, backward in time from observed data, to a most recent common ancestor. However, in many cases, the computational time and variance of estimators are often too high to make standard approaches useful. In this paper, we propose to stop the simulation, subsequently yielding biased estimates of the likelihood surface. The bias is investigated from a theoretical point of view. Results from simulation studies are also given to investigate the balance between loss of accuracy, saving in computing time and variance reduction.

scholarly journals Numerical Model for the Analysis of Thermal Transients in District Heating Networks

2020 ◽  
Vol 197 ◽  
pp. 01004
Author(s):  
Martina Capone ◽  
Elisa Guelpa ◽  
Vittorio Verda
Keyword(s):  
Carbon Dioxide Emissions ◽  
Renewable Energy Sources ◽  
Management Strategies ◽  
District Heating ◽  
Equivalent Model ◽  
Computational Time ◽  
Physical Parameters ◽  
Thermal Transients ◽  
Proposed Model ◽  
Wide Range

As District Heating (DH) networks are experiencing an evolution towards the so-called 4th generation, there is a need to update the currently used models to take into account the ever-increasing complexity of this technology. Indeed, to further improve the reduction in energy consumption and carbon-dioxide emissions, a wide range of technologies and management strategies are being introduced within district heating, such as a large exploitation of Renewable Energy Sources (RES). As a consequence, thermal transients assume a major importance, posing the need to redefine the relevant physical parameters and to develop a model which accurately describes their behaviour. In this framework, this paper proposes a quantitative analysis of the influence of the pipe heat-capacity on the model. Moreover, an equivalent-model, which is able to take into account the two heat capacities of steel and water in just one equation, is proposed and compared with two commonly used approaches. One of the features of the proposed model is the suitability for application to large networks. To prove its capabilities, an application to the Turin district heating network, which is among the largest systems in Europe, is proposed. Results show significant improvements in terms of accuracy over computational time ratio.

scholarly journals A Multidimensional and Multiscale Model for Pressure Analysis in a Reservoir-Pipe-Valve System

2018 ◽  
Author(s):  
Feng Jie Zheng ◽  
Fu Zheng Qu ◽  
Xue Guan Song
Keyword(s):  
Pressure Fluctuation ◽  
Large Scale ◽  
Three Dimensional ◽  
Industrial Process ◽  
Multiscale Model ◽  
Computational Time ◽  
Small Scale ◽  
Cfd Model ◽  
Computationally Efficient ◽  
Proposed Model

Reservoir-pipe-valve (RPV) systems are widely used in many industrial process. The pressure in an RPV system plays an important role in the safe operation of the system, especially during the sudden operation such as rapid valve opening/closing. To investigate the pressure especially the pressure fluctuation in an RPV system, a multidimensional and multiscale model combining the method of characteristics (MOC) and computational fluid dynamics (CFD) method is proposed. In the model, the reservoir is modeled by a zero-dimensional virtual point, the pipe is modeled by a one-dimensional MOC, and the valve is modeled by a three-dimensional CFD model. An interface model is used to connect the multidimensional and multiscale model. Based on the model, a transient simulation of the turbulent flow in an RPV system is conducted, in which not only the pressure fluctuation in the pipe but also the detailed pressure distribution in the valve are obtained. The results show that the proposed model is in good agreement with the full CFD model in both large-scale and small-scale spaces. Moreover, the proposed model is more computationally efficient than the CFD model, which provides a feasibility in the analysis of complex RPV system within an affordable computational time.

scholarly journals Particle Filter with Gaussian Weighting for Vehicle Tracking

2011 ◽  
Vol 15 (6) ◽  
pp. 681-686
Author(s):  
Indah Agustien Siradjuddin ◽  
◽  
Muhammad Rahmat Widyanto ◽  
Keyword(s):  
Particle Filter ◽  
Object Tracking ◽  
Gaussian Distribution ◽  
Likelihood Function ◽  
Target Object ◽  
Video Data ◽  
Vehicle Tracking ◽  
Computational Time ◽  
Filter Method ◽  
Vehicle Motion

To track vehicle motion in data video, particle filter with Gaussian weighting is proposed. This method consists of four main stages. First, particles are generated to predict target’s location. Second, certain particles are searched and these particles are used to build Gaussian distribution. Third, weight of all particles is calculated based on Gaussian distribution. Fourth, particles are updated based on each weight. The proposed method could reduce computational time of tracking compared to that of conventional method of particle filter, since the proposed method does not have to calculate all particles weight using likelihood function. This method has been tested on video data with car as a target object. In average, this proposed method of particle filter is 60.61% times faster than particle filter method meanwhile the accuracy of tracking with this newmethod is comparable with particle filter method, which reach up to 86.87%. Hence this method is promising for real time object tracking application.

scholarly journals A Multidimensional and Multiscale Model for Pressure Analysis in a Reservoir-Pipe-Valve System

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Feng Jie Zheng ◽  
Chao Yong Zong ◽  
William Dempster ◽  
Fu Zheng Qu ◽  
Xue Guan Song
Keyword(s):  
Large Scale ◽  
Pressure Fluctuations ◽  
Three Dimensional ◽  
Multiscale Model ◽  
Computational Time ◽  
Small Scale ◽  
Dimensional System ◽  
Cfd Model ◽  
Computationally Efficient ◽  
Proposed Model

Reservoir-pipe-valve (RPV) systems are widely used in many industrial processes. The pressure in an RPV system plays an important role in the safe operation of the system, especially during the sudden operations such as rapid valve opening or closing. To investigate the pressure response, with particular interest in the pressure fluctuations in an RPV system, a multidimensional and multiscale model combining the method of characteristics (MOC) and computational fluid dynamics (CFD) method is proposed. In the model, the reservoir is modeled as a zero-dimensional virtual point, the pipe is modeled as a one-dimensional system using the MOC, and the valve is modeled using a three-dimensional CFD model. An interface model is used to connect the multidimensional and multiscale model. Based on the model, a transient simulation of the turbulent flow in an RPV system is conducted in which not only the pressure fluctuation in the pipe but also the detailed pressure distribution in the valve is obtained. The results show that the proposed model is in good agreement when compared with a high fidelity CFD model used to represent both large-scale and small-scale spaces. As expected, the proposed model is significantly more computationally efficient than the CFD model. This demonstrates the feasibility of analyzing complex RPV systems within an affordable computational time.

scholarly journals Classification & Feature extraction of Brain tumor from MRI Images using Modified ANN Approach

2021 ◽  
Vol 9 (2) ◽  
pp. 10-15
Author(s):  
Harendra Singh ◽  
Roop Singh Solanki
Keyword(s):  
Feature Extraction ◽  
Brain Tumor ◽  
Computational Time ◽  
Discrete Wavelet ◽  
Classification Feature ◽  
Proposed Model ◽  
Magnetic Resonance Imaging Mri ◽  
Artificial Neural Network Ann ◽  
High Degree

In this research paper, a new modified approach is proposed for brain tumor classification as well as feature extraction from Magnetic Resonance Imaging (MRI) after pre-processing of the images. The discrete wavelet transformation (DWT) technique is used for feature extraction from MRI images and Artificial Neural Network (ANN) is used for the classification of the type of tumor according to extracted features. Mean, Standard deviation, Variance, Entropy, Skewness, Homogeneity, Contrast, Correlation are the main features used to classify the type of tumor. The proposed model can give a better result in comparison with other available techniques in less computational time as well as a high degree of accuracy. The training and testing accuracies of the proposed model are 100% and 98.20% with a 98.70 % degree of precision respectively.

scholarly journals Bayesian Derivative Order Estimation for a Fractional Logistic Model

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 109
Author(s):  
Francisco J. Ariza-Hernandez ◽  
Martin P. Arciga-Alejandre ◽  
Jorge Sanchez-Ortiz ◽  
Alberto Fleitas-Imbert
Keyword(s):  
Inverse Problem ◽  
Logistic Model ◽  
Likelihood Function ◽  
Synthetic Data ◽  
Real Data ◽  
Posterior Distributions ◽  
Rate Parameter ◽  
Order Estimation ◽  
Proposed Model ◽  
Derivative Order

In this paper, we consider the inverse problem of derivative order estimation in a fractional logistic model. In order to solve the direct problem, we use the Grünwald-Letnikov fractional derivative, then the inverse problem is tackled within a Bayesian perspective. To construct the likelihood function, we propose an explicit numerical scheme based on the truncated series of the derivative definition. By MCMC samples of the marginal posterior distributions, we estimate the order of the derivative and the growth rate parameter in the dynamic model, as well as the noise in the observations. To evaluate the methodology, a simulation was performed using synthetic data, where the bias and mean square error are calculated, the results give evidence of the effectiveness for the method and the suitable performance of the proposed model. Moreover, an example with real data is presented as evidence of the relevance of using a fractional model.

scholarly journals Heterogeneous individual risk modelling of recurrent events

Biometrika ◽  
2020 ◽  
Author(s):  
Huijuan Ma ◽  
Limin Peng ◽  
Chiung-Yu Huang ◽  
Haoda Fu
Keyword(s):  
Recurrent Events ◽  
Asymptotic Properties ◽  
Dynamic Modelling ◽  
Individual Risk ◽  
Simulation Studies ◽  
Finite Sample ◽  
Risk Modelling ◽  
Modelling Framework ◽  
Proposed Model

Summary Progression of chronic disease is often manifested by repeated occurrences of disease-related events over time. Delineating the heterogeneity in the risk of such recurrent events can provide valuable scientific insight for guiding customized disease management. We propose a new sensible measure of individual risk of recurrent events and present a dynamic modelling framework thereof, which accounts for both observed covariates and unobservable frailty. The proposed modelling requires no distributional specification of the unobservable frailty, while permitting exploration of the dynamic effects of the observed covariates. We develop estimation and inference procedures for the proposed model through a novel adaptation of the principle of conditional score. The asymptotic properties of the proposed estimator, including the uniform consistency and weak convergence, are established. Extensive simulation studies demonstrate satisfactory finite-sample performance of the proposed method. We illustrate the practical utility of the new method via an application to a diabetes clinical trial that explores the risk patterns of hypoglycemia in type 2 diabetes patients.

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