Abstract: The demand for renewable energy is significantly increasing, major investments are being supplied to the wind power generation industry as a leading source of clean energy. The wind energy sector is entirely dependable and driven by the prediction of wind speed, which by the nature of wind is very stochastic and widely random. This s0tudy employs deep multi-fidelity Gaussian process regression, used to predict wind speeds for medium term time horizons. Data of the RUNE experiment in the west coast of Denmark were provided by the Technical University of Denmark, which represent the wind speed across the study area from the period between December 2015 and March 2016. The study aims to investigate the effect of pre-processing the data by denoising the signal using empirical wavelet transform (EWT) and engaging the vector components of wind speed to increase the number of input data layers for data fusion using deep multi-fidelity Gaussian process regression (GPR). The outcomes were compared using root mean square error (RMSE) and the results demonstrated a significant increase in the accuracy of predictions which demonstrated that using vector components of the wind speed as additional predictors exhibits more accurate predictions than strategies that ignore them, reflecting the importance of the inclusion of all sub data and pre-processing signals for wind speed forecasting models.
Abstract: In sports, individuals and teams are typically interested
in final rankings. Final results, such as times or distances, dictate
these rankings, also known as places. Places can be further associated
with ordered random variables, commonly referred to as order
statistics. In this work, we introduce a simple, yet accurate order
statistical ordinal regression function that predicts relay race places
with changeover-times. We call this function the Fenton-Wilkinson
Order Statistics model. This model is built on the following educated
assumption: individual leg-times follow log-normal distributions.
Moreover, our key idea is to utilize Fenton-Wilkinson approximations
of changeover-times alongside an estimator for the total number
of teams as in the notorious German tank problem. This original
place regression function is sigmoidal and thus correctly predicts
the existence of a small number of elite teams that significantly
outperform the rest of the teams. Our model also describes how place
increases linearly with changeover-time at the inflection point of the
log-normal distribution function. With real-world data from Jukola
2019, a massive orienteering relay race, the model is shown to be
highly accurate even when the size of the training set is only 5%
of the whole data set. Numerical results also show that our model
exhibits smaller place prediction root-mean-square-errors than linear
regression, mord regression and Gaussian process regression.
Abstract: Soil moisture content is a key variable in many environmental sciences. Even though it represents a small proportion of the liquid freshwater on Earth, it modulates interactions between the land surface and the atmosphere, thereby influencing climate and weather. Accurate modeling of the above processes depends on the ability to provide a proper spatial characterization of soil moisture. The measurement of soil moisture content allows assessment of soil water resources in the field of hydrology and agronomy. The second parameter in interaction with the radar signal is the geometric structure of the soil. Most traditional electromagnetic models consider natural surfaces as single scale zero mean stationary Gaussian random processes. Roughness behavior is characterized by statistical parameters like the Root Mean Square (RMS) height and the correlation length. Then, the main problem is that the agreement between experimental measurements and theoretical values is usually poor due to the large variability of the correlation function, and as a consequence, backscattering models have often failed to predict correctly backscattering. In this study, surfaces are considered as band-limited fractal random processes corresponding to a superposition of a finite number of one-dimensional Gaussian process each one having a spatial scale. Multiscale roughness is characterized by two parameters, the first one is proportional to the RMS height, and the other one is related to the fractal dimension. Soil moisture is related to the complex dielectric constant. This multiscale description has been adapted to two-dimensional profiles using the bi-dimensional wavelet transform and the Mallat algorithm to describe more correctly natural surfaces. We characterize the soil surfaces and sub-surfaces by a three layers geo-electrical model. The upper layer is described by its dielectric constant, thickness, a multiscale bi-dimensional surface roughness model by using the wavelet transform and the Mallat algorithm, and volume scattering parameters. The lower layer is divided into three fictive layers separated by an assumed plane interface. These three layers were modeled by an effective medium characterized by an apparent effective dielectric constant taking into account the presence of air pockets in the soil. We have adopted the 2D multiscale three layers small perturbations model including, firstly air pockets in the soil sub-structure, and then a vegetable canopy in the soil surface structure, that is to simulate the radar backscattering. A sensitivity analysis of backscattering coefficient dependence on multiscale roughness and new soil moisture has been performed. Later, we proposed to change the dielectric constant of the multilayer medium because it takes into account the different moisture values of each layer in the soil. A sensitivity analysis of the backscattering coefficient, including the air pockets in the volume structure with respect to the multiscale roughness parameters and the apparent dielectric constant, was carried out. Finally, we proposed to study the behavior of the backscattering coefficient of the radar on a soil having a vegetable layer in its surface structure.
Abstract: Modelling realized volatility with high-frequency returns is popular as it is an unbiased and efficient estimator of return volatility. A computationally simple model is fitting the logarithms of the realized volatilities with a fractionally integrated long-memory Gaussian process. The Gaussianity assumption simplifies the parameter estimation using the Whittle approximation. Nonetheless, this assumption may not be met in the finite samples and there may be a need to normalize the financial series. Based on the empirical indices S&P500 and DAX, this paper examines the performance of the linear volatility model pre-treated with normalization compared to its existing counterpart. The empirical results show that by including normalization as a pre-treatment procedure, the forecast performance outperforms the existing model in terms of statistical and economic evaluations.
Abstract: The wind is a random variable difficult to master, for this, we developed a mathematical and statistical methods enable to modeling and forecast wind power. Gaussian Processes (GP) is one of the most widely used families of stochastic processes for modeling dependent data observed over time, or space or time and space. GP is an underlying process formed by unrecognized operator’s uses to solve a problem. The purpose of this paper is to present how to forecast wind power by using the GP. The Gaussian process method for forecasting are presented. To validate the presented approach, a simulation under the MATLAB environment has been given.
Abstract: In this work, we present a Bayesian non-parametric
approach to model the motion control of ATVs. The motion control
model is based on a Dirichlet Process-Gaussian Process (DP-GP)
mixture model. The DP-GP mixture model provides a flexible
representation of patterns of control manoeuvres along trajectories
of different lengths and discretizations. The model also estimates the
number of patterns, sufficient for modeling the dynamics of the ATV.
Abstract: We present probabilistic multinomial Dirichlet
classification model for multidimensional data and Gaussian process
priors. Here, we have considered efficient computational method that
can be used to obtain the approximate posteriors for latent variables
and parameters needed to define the multiclass Gaussian process
classification model. We first investigated the process of inducing a
posterior distribution for various parameters and latent function by
using the variational Bayesian approximations and important sampling
method, and next we derived a predictive distribution of latent
function needed to classify new samples. The proposed model is
applied to classify the synthetic multivariate dataset in order to verify
the performance of our model. Experiment result shows that our model
is more accurate than the other approximation methods.
Abstract: In this paper, we propose the variational EM inference
algorithm for the multi-class Gaussian process classification model
that can be used in the field of human behavior recognition. This
algorithm can drive simultaneously both a posterior distribution of a
latent function and estimators of hyper-parameters in a Gaussian
process classification model with multiclass. Our algorithm is based
on the Laplace approximation (LA) technique and variational EM
framework. This is performed in two steps: called expectation and
maximization steps. First, in the expectation step, using the Bayesian
formula and LA technique, we derive approximately the posterior
distribution of the latent function indicating the possibility that each
observation belongs to a certain class in the Gaussian process
classification model. Second, in the maximization step, using a derived
posterior distribution of latent function, we compute the maximum
likelihood estimator for hyper-parameters of a covariance matrix
necessary to define prior distribution for latent function. These two
steps iteratively repeat until a convergence condition satisfies.
Moreover, we apply the proposed algorithm with human action
classification problem using a public database, namely, the KTH
human action data set. Experimental results reveal that the proposed
algorithm shows good performance on this data set.
Abstract: In this paper, we considered and applied parametric
modeling for some experimental data of dynamical system. In this
study, we investigated the different distribution of output
measurement from some dynamical systems. Also, with variance
processing in experimental data we obtained the region of
nonlinearity in experimental data and then identification of output
section is applied in different situation and data distribution. Finally,
the effect of the spanning the measurement such as variance to
identification and limitation of this approach is explained.
Abstract: This paper proposes an application of probabilistic technique, namely Gaussian process regression, for estimating an optimal sequence of the single machine with total weighted tardiness (SMTWT) scheduling problem. In this work, the Gaussian process regression (GPR) model is utilized to predict an optimal sequence of the SMTWT problem, and its solution is improved by using an iterated local search based on simulated annealing scheme, called GPRISA algorithm. The results show that the proposed GPRISA method achieves a very good performance and a reasonable trade-off between solution quality and time consumption. Moreover, in the comparison of deviation from the best-known solution, the proposed mechanism noticeably outperforms the recently existing approaches.
Abstract: This paper presents a Gaussian process model-based
short-term electric load forecasting. The Gaussian process model is
a nonparametric model and the output of the model has Gaussian
distribution with mean and variance. The multiple Gaussian process
models as every hour ahead predictors are used to forecast future
electric load demands up to 24 hours ahead in accordance with the
direct forecasting approach. The separable least-squares approach that
combines the linear least-squares method and genetic algorithm is
applied to train these Gaussian process models. Simulation results
are shown to demonstrate the effectiveness of the proposed electric
load forecasting.
Abstract: This paper presents a nonparametric identification of
continuous-time nonlinear systems by using a Gaussian process
(GP) model. The GP prior model is trained by artificial bee colony
algorithm. The nonlinear function of the objective system is estimated
as the predictive mean function of the GP, and the confidence
measure of the estimated nonlinear function is given by the predictive
covariance of the GP. The proposed identification method is applied
to modeling of a simplified electric power system. Simulation results
are shown to demonstrate the effectiveness of the proposed method.
Abstract: The paper investigates the potential of support vector
machines and Gaussian process based regression approaches to
model the oxygen–transfer capacity from experimental data of
multiple plunging jets oxygenation systems. The results suggest the
utility of both the modeling techniques in the prediction of the
overall volumetric oxygen transfer coefficient (KLa) from operational
parameters of multiple plunging jets oxygenation system. The
correlation coefficient root mean square error and coefficient of
determination values of 0.971, 0.002 and 0.945 respectively were
achieved by support vector machine in comparison to values of
0.960, 0.002 and 0.920 respectively achieved by Gaussian process
regression. Further, the performances of both these regression
approaches in predicting the overall volumetric oxygen transfer
coefficient was compared with the empirical relationship for multiple
plunging jets. A comparison of results suggests that support vector
machines approach works well in comparison to both empirical
relationship and Gaussian process approaches, and could successfully
be employed in modeling oxygen-transfer.
Abstract: Mathematical justifications are given for a simulation technique of multivariate nonGaussian random processes and fields based on Rosenblatt-s transformation of Gaussian processes. Different types of convergences are given for the approaching sequence. Moreover an original numerical method is proposed in order to solve the functional equation yielding the underlying Gaussian process autocorrelation function.