This article presents a novel data-based approach to investigate the non-Gaussian stochastic distribution control problem. As the motivation of this article, the existing methods have been summarised ...regarding to the drawbacks, for example, neural network weights training for unknown stochastic distribution and so on. To overcome these disadvantages, a new transformation for dynamic probability density function is given by kernel density estimation using interpolation. Based upon this transformation, a representative model has been developed while the stochastic distribution control problem has been transformed into an optimization problem. Then, data-based direct optimization and identification-based indirect optimization have been proposed. In addition, the convergences of the presented algorithms are analysed and the effectiveness of these algorithms has been evaluated by numerical examples. In summary, the contributions of this article are as follows: 1) a new data-based probability density function transformation is given; 2) the optimization algorithms are given based on the presented model; and 3) a new research framework is demonstrated as the potential extensions to the existing stochastic distribution control.
Most bias correction algorithms used in climatology, for example quantile mapping, are applied to univariate time series. They neglect the dependence between different variables. Those that are ...multivariate often correct only limited measures of joint dependence, such as Pearson or Spearman rank correlation. Here, an image processing technique designed to transfer colour information from one image to another—the
N
-dimensional probability density function transform—is adapted for use as a multivariate bias correction algorithm (MBCn) for climate model projections/predictions of multiple climate variables. MBCn is a multivariate generalization of quantile mapping that transfers all aspects of an observed continuous multivariate distribution to the corresponding multivariate distribution of variables from a climate model. When applied to climate model projections, changes in quantiles of each variable between the historical and projection period are also preserved. The MBCn algorithm is demonstrated on three case studies. First, the method is applied to an image processing example with characteristics that mimic a climate projection problem. Second, MBCn is used to correct a suite of 3-hourly surface meteorological variables from the Canadian Centre for Climate Modelling and Analysis Regional Climate Model (CanRCM4) across a North American domain. Components of the Canadian Forest Fire Weather Index (FWI) System, a complicated set of multivariate indices that characterizes the risk of wildfire, are then calculated and verified against observed values. Third, MBCn is used to correct biases in the spatial dependence structure of CanRCM4 precipitation fields. Results are compared against a univariate quantile mapping algorithm, which neglects the dependence between variables, and two multivariate bias correction algorithms, each of which corrects a different form of inter-variable correlation structure. MBCn outperforms these alternatives, often by a large margin, particularly for annual maxima of the FWI distribution and spatiotemporal autocorrelation of precipitation fields.
This paper is concerned with a class of discrete-time semi-Markov jump linear systems (S-MJLSs) subject to exponentially modulated periodic (EMP) probability density function (PDF) of sojourn time, ...and the problems of stability and stabilization are addressed. Setting a relatively large period, the considered systems are capable of approximating the general S-MJLSs (without any requirements on sojourn-time PDFs) for which numerically testable stability and stabilization conditions are rather difficult to obtain. Necessary and sufficient criterion for mean square stability of the general S-MJLSs is first derived, which involves an infinite number of conditions and as such not checkable. However, the developments lay a foundation to further establish the numerically testable conditions for the systems when the PDF of sojourn time is EMP albeit the sojourn time can tend to infinity. The derivations explicitly depend on the PDF of sojourn time, which circumvents the difficulty in obtaining the memory transition probabilities of S-MJLSs. The adopted Lyapunov function is sojourn-time-dependent (STD), by which the existence conditions of STD controller are developed as well using certain techniques that can eliminate the terms of power of matrices in the stability conditions. Two illustrative examples including a class of population ecological systems are presented to show the validity and applicability of the developed theoretical results.
The existence of wind power forecast errors is one of the most challenging issues for wind power system operation. It is difficult to find a reasonable method for the representation of forecast ...errors and apply it in scheduling. In this paper, a probability distribution model named "versatile distribution" is formulated and developed along with its properties and applications. The model can well represent forecast errors for all forecast timescales and magnitudes. The incorporation of the model in economic dispatch (ED) problems can simplify the wind-induced uncertainties via a few analytical terms in the problem formulation. The ED problem with wind power could hence be solved by the classical optimization methods, such as sequential linear programming which has been widely accepted by industry for solving ED problems. Discussions are also extended on the incorporation of the proposed versatile distribution into unit commitment problems. The results show that the new distribution is more effective than other commonly used distributions (i.e., Gaussian and Beta) with more accurate representation of forecast errors and better formulation and solution of ED problems.
Vehicles today are equipped with control systems that improve their handling and stability. Knowledge of road bank angle and vehicle parameters is crucial for good behavior in this type of control. ...This paper develops a new method for estimating different states, such as vehicle roll angle, road bank angle, and vehicle parameters. This method combines a dual Kalman filter with a probability density function truncation method to consider the parameter physical limitations. Experimental results show the effectiveness of the proposed method and demonstrate that the incorporation of parameter constraints improves its estimation accuracy. The proposed method provides an estimation of the parameters and the states' physical meaning and the stable values within the real boundary limits in contrast to other estimation methods.
This paper introduces a novel EMD interval thresholding (EMD-IT) denoising, where relevant modes are selected using a l2-norm measure between the probability density function (pdf) of the input and ...that of each mode, thresholds are estimated by the characteristics of fractional Gaussian noise (fGn) through EMD. To solve the problem of more relevant modes included when the signal is corrupted by fGn with the H increase, a modified l2-norm method was given. The computational complexity of EMD-IT denoising is also analyzed. And the time complexity of it is equal to that of EMD. Numerical simulation and real data test were carried out to evaluate the effectiveness of the proposed method. Other traditional denoisings, such as correlation-based EMD partial reconstruction (EMD-PR), EMD direct thresholding (EMD-DT) and NeighCoeff-db4 wavelet denoising are investigated to provide a comparison with the proposed one. Simulation and test results show its superior performance over other traditional denoisings in whole.
•Original l2-norm measure is modified to solve more relevant modes selected.•EMD-IT with pdf is proposed to denoise the white Gaussian noise and fGn.•The selection of threshold is analyzed based on the fGn decomposition.•The order of time complexity of EMD-based denoising is equal to that of EMD.
In recent years, there has been an increasing use of fractional differential equations due to their ability to effectively represent various engineering phenomena, including viscoelasticity, heat ...transport, non-local continuum, and others. These equations take into account certain effects that cannot be accurately predicted using classical differential equations.
This paper provides a comprehensive analysis of the fractional compound motion, specifically focusing on the response of a one-term fractional differential equation that is excited by a Poissonian white noise process. The present study introduces a straightforward equation for the probability density function of fractional compound motion. The validity of this equation is subsequently confirmed by the execution of various numerical simulations. Furthermore, a comprehensive analysis is conducted on the self-similarity of fractional compound motion, demonstrating that the phenomenon can be regarded as self-similar in weak sense. This characteristic can be effectively employed to mitigate the loss of Markovianity in fractional differential equations.
•The PDF of the fCM tends to be Gaussian for instants sufficiently distant from zero.•For instants distant from zero the PDF of the fCM tends to the PDF of a fBM.•FCM tends to be self-similar for instants sufficiently distant from zero.•Wake self-similarity of fCM allows to overcome the loss of Markovianity.
A gamma probability density function (pdf) is shown to be an alternative to model the distribution of the magnitudes of high-resolution, i.e., wavelength-resolution, synthetic aperture radar (SAR) ...images. As investigated in this paper, it is more appropriate and more realistic statistical in comparison with, e.g., Rayleigh. A bivariate gamma pdf is considered for developing a statistical hypothesis test for wavelength-resolution incoherent SAR change detection. The practical issues in implementation of statistical hypothesis test, such as assumptions on target magnitudes, estimations for scale and shape parameters, and implementation of modified Bessel function, are addressed. This paper also proposes a simple processing scheme for incoherent change detection to validate the proposed statistical hypothesis test. The proposal was experimented with 24 CARABAS data sets. With an average detection probability of 96%, the false alarm rate is only 0.47 per square kilometer.
Riparian or aquatic vegetation thrives with seasons. The understanding of canopies' Submergence‐Ratio (SR = stem height/water depth) influence on suspended sediment transport is still limited. Thus, ...Large Eddy Simulations coupled with the Discrete Phase Method are used to investigate the particles' three‐dimensional distribution in a partially vegetated straight channel. The spanwise distribution of particles are quantified by the probability density function (PDF), showing a non‐uniformity of particles in time as quantified by the PDF variance. We found that (a) with SR rising, the particles' depletion effects exerted by the vegetation‐side mixing layer is improved along the interface between vegetated and vegetation‐side bare channel region. However, the SR has little effect on the variance of the particles' PDF in the spanwise direction when the mixing layer is fully developed. (b) During the developing stage of the over‐canopy mixing layer, submerged vegetation with higher SR gains a stronger upwards (vertical) entrainment capability. The case (SR = 60%) has a higher sediment concentration than other cases in the fully developed vertical mixing layer region over canopy. (c) The vertical suspension of particles in the vegetation‐side bare channel region is analyzed. Particles migrating from the vegetated region are entrained into the vegetation‐side bare channel region by turbulent structures. Nevertheless, the vertical concentration profile is more uniform in the vegetated region than in the vegetation‐side bare channel at the same streamwise location. The cases SR = 40% and 60% still have higher sediment concentration than other cases in the vegetation‐side bare channel's upper region.
Plain Language Summary
Rivers are the blood vessels of the Earth, constantly transporting water, sediments, biomes, etc., and constantly shaping the surface of the Earth. The vegetation in the river, through its physical, chemical and biological functions, has a profound impact on the river's role in transporting sediment. In different seasons of the year, the water level of rivers and the height of aquatic plants change. The purpose of this study is to reveal the effect of the height of vegetation relative to water depth on the movement of sediment particles in water flow. The UK national high‐performance computer was used to carry out high‐fidelity simulations of sediment transport in a straight with partially vegetated covered channel. We found that the increase of the relative height of the vegetation highly influence the distribution of the particles in the spanwise of the channel. In the present vegetation condition, the sparse vegetation whose height is slightly over the half flow depth promote higher sediment concentration in the high location of the channel flow (away from the channel bottom) than other vegetation height conditions in the vegetated region. Interestingly, the sediment concentration in the vegetation‐side bare channel region almost has the same characteristics, namely, vegetation with half water depth have the strongest ability to improve the sediment concentration in the upper region of the bare channel flow. The results of this research are very beneficial for green ecological management of river sediment and the management of sediment deposition in key sections of rivers.
Key Points
Relationship between submergence ratio and sediment's transport is investigated for vegetated and non‐vegetated bare channel regions
Case Submergence Ratio (SR) = 60% has higher normalized concentration than other cases (such as SR = 20%, 40%, and 80%) in the upper layer of a fully developed vertical mixing layer
Vertical suspension of particles in the non‐vegetated bare channel region occurs due to presence of riparian vegetation along the channel
In solving the electrical power systems economic dispatch (ED) problem, the goal is to find the optimal allocation of output power among the various generators available to serve the system load. ...With the continuing search for alternatives to conventional energy sources, it is necessary to include wind energy conversion system (WECS) generators in the ED problem. This paper develops a model to include the WECS in the ED problem, and in addition to the classic economic dispatch factors, factors to account for both overestimation and underestimation of available wind power are included. With the stochastic wind speed characterization based on the Weibull probability density function, the optimization problem is numerically solved for a scenario involving two conventional and two wind-powered generators. Optimal solutions are presented for various values of the input parameters, and these solutions demonstrate that the allocation of system generation capacity may be influenced by multipliers related to the risk of overestimation and to the cost of underestimation of available wind power.
PDF
