Search results for: optimal estimation

Authors: Alia Alghosoun, Nabil El Moçayd, Mohammed Seaid

Abstract:

Modeling dam-break flows over non-flat beds requires an accurate representation of the topography which is the main source of uncertainty in the model. Therefore, developing robust and accurate techniques for reconstructing topography in this class of problems would reduce the uncertainty in the flow system. In many hydraulic applications, experimental techniques have been widely used to measure the bed topography. In practice, experimental work in hydraulics may be very demanding in both time and cost. Meanwhile, computational hydraulics have served as an alternative for laboratory and field experiments. Unlike the forward problem, the inverse problem is used to identify the bed parameters from the given experimental data. In this case, the shallow water equations used for modeling the hydraulics need to be rearranged in a way that the model parameters can be evaluated from measured data. However, this approach is not always possible and it suffers from stability restrictions. In the present work, we propose an adaptive optimal control technique to numerically identify the underlying bed topography from a given set of free-surface observation data. In this approach, a minimization function is defined to iteratively determine the model parameters. The proposed technique can be interpreted as a fractional-stage scheme. In the first stage, the forward problem is solved to determine the measurable parameters from known data. In the second stage, the adaptive control Ensemble Kalman Filter is implemented to combine the optimality of observation data in order to obtain the accurate estimation of the topography. The main features of this method are on one hand, the ability to solve for different complex geometries with no need for any rearrangements in the original model to rewrite it in an explicit form. On the other hand, its achievement of strong stability for simulations of flows in different regimes containing shocks or discontinuities over any geometry. Numerical results are presented for a dam-break flow problem over non-flat bed using different solvers for the shallow water equations. The robustness of the proposed method is investigated using different numbers of loops, sensitivity parameters, initial samples and location of observations. The obtained results demonstrate high reliability and accuracy of the proposed techniques.

Keywords: Optimal control, ensemble Kalman Filter, topography reconstruction, data assimilation, shallow water equations.

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Authors: Yannan Wu, An Chen, Yan Zhao

Abstract:

Termination Mechanism is an indispensible part of the emergency management mechanism. Despite of its importance in both theory and practice, it is almost a brand new field for researching. The concept of termination mechanism is proposed firstly in this paper, and the design and implementation which are helpful to guarantee the effect and integrity of emergency management are discussed secondly. Starting with introduction of the problems caused by absent termination and incorrect termination, the essence of termination mechanism is analyzed, a model based on Optimal Stopping Theory is constructed and the termination index is given. The model could be applied to find the best termination time point.. Termination decision should not only be concerned in termination stage, but also in the whole emergency management process, which makes it a dynamic decision making process. Besides, the main subjects and the procedure of termination are illustrated after the termination time point is given. Some future works are discussed lastly.

Keywords: Emergency management, Termination Mechanism, Optimal Termination Model, Decision Making, Optimal StoppingTheory.

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Authors: Christian Rathgeber, Franz Winkler, Xiaoyu Kang, Steffen Müller

Abstract:

In this contribution two approaches for calculating optimal trajectories for highly automated vehicles are presented and compared. The first one is based on a non-linear vehicle model, used for evaluation. The second one is based on a simplified model and can be implemented on a current ECU. In usual driving situations both approaches show very similar results.

Keywords: Trajectory planning, direct method, indirect method, highly automated driving.

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Authors: Liyuan Wang, Shouming Zhong

Abstract:

In this paper, the design problem of state estimator for neural networks with the mixed time-varying delays are investigated by constructing appropriate Lyapunov-Krasovskii functionals and using some effective mathematical techniques. In order to derive several conditions to guarantee the estimation error systems to be globally exponential stable, we transform the considered systems into the neural-type time-delay systems. Then with a set of linear inequalities(LMIs), we can obtain the stable criteria. Finally, three numerical examples are given to show the effectiveness and less conservatism of the proposed criterion.

Keywords: State estimator, Neural networks, Globally exponential stability.

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Authors: B. Baigzadeh, V.Nazarzehi, H.Khaloozadeh

Abstract:

The two cart inverted pendulum system is a good bench mark for testing the performance of system dynamics and control engineering principles. Devasia introduced this system to study the asymptotic tracking problem for nonlinear systems. In this paper the problem of asymptotic tracking of the two-cart with an inverted-pendulum system to a sinusoidal reference inputs via introducing a novel method for solving finite-horizon nonlinear optimal control problems is presented. In this method, an iterative method applied to state dependent Riccati equation (SDRE) to obtain a reliable algorithm. The superiority of this technique has been shown by simulation and comparison with the nonlinear approach.

Keywords: Nonlinear optimal control, State dependent Riccatiequation, Asymptotic tracking, inverted pendulum

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Authors: N. Valliammal, S.N. Geethalakshmi

Abstract:

This paper describes an optimal approach for feature subset selection to classify the leaves based on Genetic Algorithm (GA) and Kernel Based Principle Component Analysis (KPCA). Due to high complexity in the selection of the optimal features, the classification has become a critical task to analyse the leaf image data. Initially the shape, texture and colour features are extracted from the leaf images. These extracted features are optimized through the separate functioning of GA and KPCA. This approach performs an intersection operation over the subsets obtained from the optimization process. Finally, the most common matching subset is forwarded to train the Support Vector Machine (SVM). Our experimental results successfully prove that the application of GA and KPCA for feature subset selection using SVM as a classifier is computationally effective and improves the accuracy of the classifier.

Keywords: Optimization, Feature extraction, Feature subset, Classification, GA, KPCA, SVM and Computation

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Authors: M. Baghdasaryan, A. Sukiasyan

Abstract:

An algorithm for estimating the stable operation conditions of the synchronous motor of the ore mill electric drive is proposed. The stable operation conditions of the synchronous motor are revealed, taking into account the estimation of the q angle change and the technological factors. The stability condition obtained allows to ensure the stable operation of the motor in the synchronous mode, taking into account the nonlinear character of the mill loading. The developed algorithm gives an opportunity to present the undesirable phenomena, arising in the electric drive system. The obtained stability condition can be successfully applied for the optimal control of the electromechanical system of the mill.

Keywords: Electric drive, synchronous motor, ore mill, stability, technological factors.

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Authors: Vu Ngoc Pi

Abstract:

In this paper, a study on the applications of the optimization and regression techniques for optimal calculation of partial ratios of helical gearboxes with second-step double gear-sets for minimal cross section dimension is introduced. From the condition of the moment equilibrium of a mechanic system including three gear units and their regular resistance condition, models for calculation of the partial ratios of helical gearboxes with second-step double gear-sets were given. Especially, by regression analysis, explicit models for calculation of the partial ratios are introduced. These models allow determining the partial ratios accurately and simply.

Keywords: Gearbox design, optimal design, helical gearbox, transmission ratio.

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Authors: Y. Areepong

Abstract:

The objective of this paper is to present explicit analytical formulas for evaluating important characteristics of Double Moving Average control chart (DMA) for Poisson distribution. The most popular characteristics of a control chart are Average Run Length ( 0 ARL ) - the mean of observations that are taken before a system is signaled to be out-of control when it is actually still incontrol, and Average Delay time ( 1 ARL ) - mean delay of true alarm times. An important property required of 0 ARL is that it should be sufficiently large when the process is in-control to reduce a number of false alarms. On the other side, if the process is actually out-ofcontrol then 1 ARL should be as small as possible. In particular, the explicit analytical formulas for evaluating 0 ARL and 1 ARL be able to get a set of optimal parameters which depend on a width of the moving average ( w ) and width of control limit ( H ) for designing DMA chart with minimum of 1 ARL

Keywords: Optimal parameters, Average Run Length, Average Delay time, Double Moving Average chart.

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Authors: Sorawit Stapornchaisit, Sidshchadhaa Aumted, Hiroshi Takami

Abstract:

In this paper, we propose a novel adaptive voltage control strategy for boost converter via Inverse LQ Servo-Control. Our presented strategy is based on an analytical formula of Inverse Linear Quadratic (ILQ) design method, which is not necessary to solve Riccati’s equation directly. The optimal and adaptive controller of the voltage control system is designed. The stability and the robust control are analyzed. Whereas, we can get the analytical solution for the optimal and robust voltage control is achieved through the natural angular velocity within a single parameter and we can change the responses easily via the ILQ control theory. Our method provides effective results as the stable responses and the response times are not drifted even if the condition is changed widely.

Keywords: Boost converter, optimal voltage control, inverse LQ design method, type-1 servo-system, adaptive control.

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Authors: Mahmoud Zarrini, R. N. Pralhad

Abstract:

In this paper, mathematical modeling of detonation in the ground is studied. Estimation of flow parameters such as velocity, maximum velocity, acceleration, maximum acceleration, shock pressure as a result of an explosion in the ground have been computed in an appropriate dynamic model approach. The variation of these parameters with the diameter of detonation place (L), density of earth or stone (¤ü), time decay of detonation (T), peak pressure (Pm), and time (t) have been analyzed. The model has been developed from the concept of underwater explosions [Refs. [1]-[3]] with appropriate changes to the present model requirements.

Keywords: Shock velocity, detonation, shock acceleration, shock pressure.

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Authors: Lokendra Singh Umrao, Ravi Shankar Singh

Abstract:

This paper presents an optimal broadcast algorithm for the hypercube networks. The main focus of the paper is the effectiveness of the algorithm in the presence of many node faults. For the optimal solution, our algorithm builds with spanning tree connecting the all nodes of the networks, through which messages are propagated from source node to remaining nodes. At any given time, maximum n − 1 nodes may fail due to crashing. We show that the hypercube networks are strongly fault-tolerant. Simulation results analyze to accomplish algorithm characteristics under many node faults. We have compared our simulation results between our proposed method and the Fu’s method. Fu’s approach cannot tolerate n − 1 faulty nodes in the worst case, but our approach can tolerate n − 1 faulty nodes.

Keywords: Fault tolerance, hypercube, broadcasting, link/node faults, routing.

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Authors: Y. N. Phang, E. F. Loh

Abstract:

Zero inflated strict arcsine model is a newly developed model which is found to be appropriate in modeling overdispersed count data. In this study, we extend zero inflated strict arcsine model to zero inflated strict arcsine regression model by taking into consideration the extra variability caused by extra zeros and covariates in count data. Maximum likelihood estimation method is used in estimating the parameters for this zero inflated strict arcsine regression model.

Keywords: Overdispersed count data, maximum likelihood estimation, simulated annealing.

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Authors: D. De-León-Escobedo, D. J. Delgado-Hernández, S. Pérez

Abstract:

A probabilistic formulation to assess the slopes safety under the hazard of strong storms is presented and illustrated through a slope in Mexico. The formulation is based on the classical safety factor (SF) used in practice to appraise the slope stability, but it is introduced the treatment of uncertainties, and the slope failure probability is calculated as the probability that SF<1. As the main hazard is the rainfall on the area, statistics of rainfall intensity and duration are considered and modeled with an exponential distribution. The expected life-cycle cost is assessed by considering a monetary value on the slope failure consequences. Alternative mitigation measures are simulated, and the formulation is used to get the measures driving to the optimal one (minimum life-cycle costs). For the example, the optimal mitigation measure is the reduction on the slope inclination angle.

Keywords: Expected life-cycle cost, failure probability, slopes failure, storms.

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Authors: Kevin Spencer G. Anglim, Zhenyu Zhang, Qingbin Gao

Abstract:

Reusable launch vehicles (RLVs) present a more environmentally-friendly approach to accessing space when compared to traditional launch vehicles that are discarded after each flight. This paper studies the recyclable nature of RLVs by presenting a solution method for determining minimum-fuel optimal trajectories using principles from optimal control theory and particle swarm optimization (PSO). This problem is formulated as a minimum-landing error powered descent problem where it is desired to move the RLV from a fixed set of initial conditions to three different sets of terminal conditions. However, unlike other powered descent studies, this paper considers the highly nonlinear effects caused by atmospheric drag, which are often ignored for studies on the Moon or on Mars. Rather than optimizing the controls directly, the throttle control is assumed to be bang-off-bang with a predetermined thrust direction for each phase of flight. The PSO method is verified in a one-dimensional comparison study, and it is then applied to the two-dimensional cases, the results of which are illustrated.

Keywords: Minimum-fuel optimal trajectory, particle swarm optimization, reusable rocket, SpaceX.

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Authors: Efstratios Doukakis, Nikolaos Petrelis

Abstract:

All climate models agree that the temperature in Greece will increase in the range of 1° to 2°C by the year 2030 and mean sea level in Mediterranean is expected to rise at the rate of 5 cm/decade. The aim of the present paper is the estimation of the coastline displacement driven by the climate change and sea level rise. In order to achieve that, all known statistical and non-statistical computational methods are employed on some Greek coastal areas. Furthermore, Kalman filtering techniques are for the first time introduced, formulated and tested. Based on all the above, shoreline change signals and noises are computed and an inter-comparison between the different methods can be deduced to help evaluating which method is most promising as far as the retrieve of shoreline change rate is concerned.

Keywords: Climate Change, Coastal Displacement, KalmanFilter

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Authors: Gye-rok Jeon, Jae-hee Jung, In-cheol Kim, Ah-young Jeon, Sang-hwa Yoon, Jung-man Son, Jae-hyung Kim, Soo-young Ye, Jung-hoon Ro, Dong-hyun Kim, Chul-han Kim

Abstract:

A analysis on the conventional the blood pressure estimation method using an oscillometric sphygmomanometer was performed through a computer simulation using an arterial pressure-volume (APV) model. Traditionally, the maximum amplitude algorithm (MAP) was applied on the oscillation waveforms of the APV model to obtain the mean arterial pressure and the characteristic ratio. The estimation of mean arterial pressure and characteristic ratio was significantly affected with the shape of the blood pressure waveforms and the cutoff frequency of high-pass filter (HPL) circuitry. Experimental errors are due to these effects when estimating blood pressure. To find out an algorithm independent from the influence of waveform shapes and parameters of HPL, the volume oscillation of the APV model and the phase shift of the oscillation with fast fourier transform (FFT) were testified while increasing the cuff pressure from 1 mmHg to 200 mmHg (1 mmHg per second). The phase shift between the ranges of volume oscillation was then only observed between the systolic and the diastolic blood pressures. The same results were also obtained from the simulations performed on two different the arterial blood pressure waveforms and one hyperthermia waveform.

Keywords: Arterial blood pressure, oscillometric method

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Authors: P. S. Prakash, S. Selvan

Abstract:

QoS Routing aims to find paths between senders and receivers satisfying the QoS requirements of the application which efficiently using the network resources and underlying routing algorithm to be able to find low-cost paths that satisfy given QoS constraints. The problem of finding least-cost routing is known to be NP-hard or complete and some algorithms have been proposed to find a near optimal solution. But these heuristics or algorithms either impose relationships among the link metrics to reduce the complexity of the problem which may limit the general applicability of the heuristic, or are too costly in terms of execution time to be applicable to large networks. In this paper, we concentrate an algorithm that finds a near-optimal solution fast and we named this algorithm as optimized Delay Constrained Routing (ODCR), which uses an adaptive path weight function together with an additional constraint imposed on the path cost, to restrict search space and hence ODCR finds near optimal solution in much quicker time.

Keywords: QoS, Delay, Routing, Optimization.

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Authors: S. Maheswari, P. Arockia Jansi Rani

Abstract:

Human action is recognized directly from the video sequences. The objective of this work is to recognize various human actions like run, jump, walk etc. Human action recognition requires some prior knowledge about actions namely, the motion estimation, foreground and background estimation. Region of interest (ROI) is extracted to identify the human in the frame. Then, optical flow technique is used to extract the motion vectors. Using the extracted features similarity measure based classification is done to recognize the action. From experimentations upon the Weizmann database, it is found that the proposed method offers a high accuracy.

Keywords: Background subtraction, human silhouette, optical flow, classification.

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Authors: Virgil Miranda, Gissele Mosqueda, Pablo Delgado, Yimesker Yihun

Abstract:

Muscular fatigue affects the muscle activation that is needed for producing the desired clinical outcome. Integrating optimal muscle relaxation periods into a variety of health care rehabilitation protocols is important to maximize the efficiency of the therapy. In this study, four muscle relaxation periods (30, 60, 90 and 120 seconds) and their effectiveness in producing consistent muscle activation of the muscle biceps brachii between sets of an elbow flexion and extension task were investigated among a sample of 10 subjects with no disabilities. The same resting periods were then utilized in a controlled exoskeleton-based exercise for a sample size of 5 subjects and have shown similar results. On average, the muscle activity of the biceps brachii decreased by 0.3% when rested for 30 seconds, and it increased by 1.25%, 0.76% and 0.82% when using muscle relaxation periods of 60, 90 and 120 seconds, respectively. The preliminary results suggest that a muscle relaxation period of about 60 seconds is needed for optimal continuous muscle activation within rehabilitation regimens. Robot-based rehabilitation is good to produce repetitive tasks with the right intensity and knowing the optimal resting period will make the automation more effective.

Keywords: Rest intervals, muscle biceps brachii, robot rehabilitation, muscle fatigue.

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Authors: Tomoaki Hashimoto

Abstract:

In recent decades, probabilistic constrained optimal control problems have attracted much attention in many research fields. Although probabilistic constraints are generally intractable in an optimization problem, several tractable methods haven been proposed to handle probabilistic constraints. In most methods, probabilistic constraints are reduced to deterministic constraints that are tractable in an optimization problem. However, there is a gap between the transformed deterministic constraints in case of known and unknown probability distribution. This paper examines the conservativeness of probabilistic constrained optimization method for unknown probability distribution. The objective of this paper is to provide a quantitative assessment of the conservatism for tractable constraints in probabilistic constrained optimization with unknown probability distribution.

Keywords: Optimal control, stochastic systems, discrete-time systems, probabilistic constraints.

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Authors: G. Sonfack, J. Mbihi, B. Lonla Moffo

Abstract:

This paper presents an optimal duty-cycle modulation (ODCM) scheme for analog-to-digital conversion (ADC) systems. The overall ODCM-Based ADC problem is decoupled into optimal DCM and digital filtering sub-problems, while taking into account constraints of mutual design parameters between the two. Using a set of three lemmas and four morphological theorems, the ODCM sub-problem is modelled as a nonlinear cost function with nonlinear constraints. Then, a weighted least p^th norm of the error between ideal and predicted frequency responses is used as a cost function for the digital filtering sub-problem. In addition, MATLAB fmincon and MATLAB iirlnorm tools are used as optimal DCM and least p^th norm solvers respectively. Furthermore, the virtual simulation scheme of an overall prototyping ODCM-based ADC system is implemented and well tested with the help of Simulink tool according to relevant set of design data, i.e., 3 KHz of modulating bandwidth, 172 KHz of maximum modulation frequency and 25 MHZ of sampling frequency. Finally, the results obtained and presented show that the ODCM-based ADC achieves under 3 KHz of modulating bandwidth: 57 dBc of SINAD (signal-to-noise and distorsion), 58 dB of SFDR (Surpious free dynamic range) -80 dBc of THD (total harmonic distorsion), and 10 bits of minimum resolution. These performance levels appear to be a great challenge within the class of oversampling ADC topologies, with 2^nd order IIR (infinite impulse response) decimation filter.

Keywords: Digital IIR filter, morphological lemmas and theorems, optimal DCM-based DAC, virtual simulation, weighted least pth norm.

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Authors: Yue-Der Lin, Wei-Ting Liu, Ching-Che Tsai, Wen-Hsiu Chen

Abstract:

PPG is a potential tool in clinical applications. Among such, the relationship between respiration and PPG signal has attracted attention in past decades. In this research, a bivariate AR spectral estimation method was utilized for the coherence analysis between these two signals. Ten healthy subjects participated in this research with signals measured at different respiratory rates. The results demonstrate that high coherence exists between respiration and PPG signal, whereas the coherence disappears in breath-holding experiments. These results imply that PPG signal reveals the respiratory information. The utilized method may provide an attractive alternative approach for the related researches.

Keywords: Coherence analysis, photoplethysmography (PPG), bivariate AR spectral estimation.

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Authors: Y. Areepong

Abstract:

The main goal of this paper is to study Statistical Process Control (SPC) with Exponentially Weighted Moving Average (EWMA) control chart when observations are serially-correlated. The characteristic of control chart is Average Run Length (ARL) which is the average number of samples taken before an action signal is given. Ideally, an acceptable ARL of in-control process should be enough large, so-called (ARL₀). Otherwise it should be small when the process is out-of-control, so-called Average of Delay Time (ARL₁) or a mean of true alarm. We find explicit formulas of ARL for EWMA control chart for Seasonal Autoregressive and Moving Average processes (SARMA) with Exponential white noise. The results of ARL obtained from explicit formula and Integral equation are in good agreement. In particular, this formulas for evaluating (ARL₀) and (ARL₁) be able to get a set of optimal parameters which depend on smoothing parameter (λ) and width of control limit (H) for designing EWMA chart with minimum of (ARL₁).

Keywords: Average Run Length1, Optimal parameters, Exponentially Weighted Moving Average (EWMA) control chart.

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Authors: Wen-Lung Huang, Shih-Pin Chen

Abstract:

This paper investigates the optimization problem of multi-product aggregate production planning (APP) with fuzzy data. From a comprehensive viewpoint of conserving the fuzziness of input information, this paper proposes a method that can completely describe the membership function of the performance measure. The idea is based on the well-known Zadeh-s extension principle which plays an important role in fuzzy theory. In the proposed solution procedure, a pair of mathematical programs parameterized by possibility level a is formulated to calculate the bounds of the optimal performance measure at a . Then the membership function of the optimal performance measure is constructed by enumerating different values of a . Solutions obtained from the proposed method contain more information, and can offer more chance to achieve the feasible disaggregate plan. This is helpful to the decision-maker in practical applications.

Keywords: fuzzy data, aggregate production planning, membership function, parametric programming

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Authors: Nemat Abazari, Ilgin Sager

Abstract:

In this paper smooth trajectories are computed in the Lie group SO(2, 1) as a motion planning problem by assigning a Frenet frame to the rigid body system to optimize the cost function of the elastic energy which is spent to track a timelike curve in Minkowski space. A method is proposed to solve a motion planning problem that minimize the integral of the square norm of Darboux vector of a timelike curve. This method uses the coordinate free Maximum Principle of Optimal control and results in the theory of integrable Hamiltonian systems. The presence of several conversed quantities inherent in these Hamiltonian systems aids in the explicit computation of the rigid body motions.

Keywords: Optimal control, Hamiltonian vector field, Darboux vector, maximum principle, lie group, Rigid body motion, Lorentz metric.

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Authors: Nikolay Nikolaev, Evgueni Smirnov

Abstract:

This paper develops an unscented grid-based filter and a smoother for accurate nonlinear modeling and analysis of time series. The filter uses unscented deterministic sampling during both the time and measurement updating phases, to approximate directly the distributions of the latent state variable. A complementary grid smoother is also made to enable computing of the likelihood. This helps us to formulate an expectation maximisation algorithm for maximum likelihood estimation of the state noise and the observation noise. Empirical investigations show that the proposed unscented grid filter/smoother compares favourably to other similar filters on nonlinear estimation tasks.

Keywords:

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Authors: Wenlong Liu, Yucheng Liu

Abstract:

This paper introduces the application of seismic wave method in earthquake prediction and early estimation. The advantages of the seismic wave method over the traditional earthquake prediction method are demonstrated. An example is presented in this study to show the accuracy and efficiency of using the seismic wave method in predicting a medium-sized earthquake swarm occurred in Wencheng, Zhejiang, China. By applying this method, correct predictions were made on the day after this earthquake swarm started and the day the maximum earthquake occurred, which provided scientific bases for governmental decision-making.

Keywords: earthquake prediction, earthquake swarm, seismicactivity method, seismic wave method, Wencheng earthquake

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Authors: Z. Saidi, A.O. Boudraa, J.C. Cexus, S. Bourennane

Abstract:

In this paper, a new time-delay estimation technique based on the cross IB-energy operator [5] is introduced. This quadratic energy detector measures how much a signal is present in another one. The location of the peak of the energy operator, corresponding to the maximum of interaction between the two signals, is the estimate of the delay. The method is a fully data-driven approach. The discrete version of the continuous-time form of the cross IBenergy operator, for its implementation, is presented. The effectiveness of the proposed method is demonstrated on real underwater acoustic signals arriving from targets and the results compared to the cross-correlation method.

Keywords: Teager-Kaiser energy operator, Cross-energyoperator, Time-Delay, Underwater acoustic signals.

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Authors: Serge B. Provost, Min Jiang

Abstract:

The density estimates considered in this paper comprise a base density and an adjustment component consisting of a linear combination of orthogonal polynomials. It is shown that, in the context of density approximation, the coefficients of the linear combination can be determined either from a moment-matching technique or a weighted least-squares approach. A kernel representation of the corresponding density estimates is obtained. Additionally, two refinements of the Kronmal-Tarter stopping criterion are proposed for determining the degree of the polynomial adjustment. By way of illustration, the density estimation methodology advocated herein is applied to two data sets.

Keywords: kernel density estimation, orthogonal polynomials, moment-based methodologies, density approximation.

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