Efficient Dynamic Analysis of a Nonlinear Wave Energy Harvester Model

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Pol D. Spanos ◽  
Felice Arena ◽  
Alessandro Richichi ◽  
Giovanni Malara
Keyword(s):  
Monte Carlo ◽  
Linear System ◽  
Wave Energy ◽  
Alternative Energy ◽  
Energy Harvester ◽  
Single Point ◽  
Computational Cost ◽  
Complex Problem ◽  
Statistical Linearization ◽  
Monte Carlo Techniques

In recent years, wave energy harvesting systems have received considerable attention as an alternative energy source. Within this class of systems, single-point harvesters are popular at least for preliminary studies and proof-of-concept analyses in particular locations. Unfortunately, the large displacements of a single-point wave energy harvester are described by a set of nonlinear equations. Further, the excitation is often characterized statistically and in terms of a relevant power spectral density (PSD) function. In the context of this complex problem, the development of efficient techniques for the calculation of reliable harvester response statistics is quite desirable, since traditional Monte Carlo techniques involve nontrivial computational cost. The paper proposes a statistical linearization technique for conducting expeditiously random vibration analyses of single-point harvesters. The technique is developed by relying on the determination of a surrogate linear system identified by minimizing the mean square error between the linear system and the nonlinear one. It is shown that the technique can be implemented via an iterative procedure, which allows calculating statistics, PSDs, and probability density functions (PDFs) of the response components. The reliability of the statistical linearization solution is assessed vis-à-vis data from relevant Monte Carlo simulations. This novel approach can be a basis for constructing computationally expeditious assessments of various design alternatives.

Nonlinear Analysis of an Oscillating Water Column Wave Energy Device in Frequency Domain via Statistical Linearization

2019 ◽  
Author(s):  
Leandro S. P. da Silva ◽  
Celso P. Pesce ◽  
Helio M. Morishita ◽  
Rodolfo T. Gonçalves
Keyword(s):  
System Dynamics ◽  
Frequency Domain ◽  
Water Column ◽  
Wave Energy ◽  
Time Domain ◽  
Computational Cost ◽  
Operating Conditions ◽  
Statistical Linearization ◽  
Large Displacements ◽  
Oscillating Water Column

Abstract Wave energy converters (WECs) are often subject to large displacements during operating conditions. Hence, nonlinearities present in numerical methods to estimate the performance of WECs must be considered for realistic predictions. These large displacements occur when the device operates on resonant conditions, which results in maximum energy conversion. The system dynamics are usually simulated via time domain models in order to being able to capture nonlinearities. However, a high computational cost is associated with those simulations. Alternatively, the present work treats the nonlinearities in the frequency domain via Statistical Linearization (SL). The SL results are compared to the Power Spectrum Density (PSD) of time domain simulations to verify the reliability of the proposed method. In this regard, the work initiates with the derivation of the governing equations of the air-chamber and the Oscillating Water Column (OWC). Then, the SL technique is presented and applied. The SL results show a satisfactory agreement for the system dynamics, mean surface elevation, mean pressure, and mean power compared to time domain simulations. Also, the SL technique produces a rapid estimation of the response, which is an effective approach for the evaluation of numerous environmental conditions and design, and further optimization procedures.

Nonlinear Analysis of an Oscillating Wave Surge Converter in Frequency Domain via Statistical Linearization

2020 ◽  
Author(s):  
Leandro S. P. da Silva ◽  
Nataliia Y. Sergiienko ◽  
Benjamin S. Cazzolato ◽  
Boyin Ding ◽  
Celso P. Pesce ◽  
...  
Keyword(s):  
Nonlinear Analysis ◽  
Frequency Domain ◽  
Wave Energy ◽  
Numerical Models ◽  
Computational Cost ◽  
Viscous Drag ◽  
Design Parameters ◽  
Statistical Linearization ◽  
Mean Power ◽  
Energy Devices

Abstract Wave energy devices operate in resonant conditions to optimize power absorption, which leads to large displacements. As a result, nonlinearities play an important role in the system dynamics and must be accounted for in the numerical models for realistic prediction of the power generated. In general, time domain (TD) simulations are employed to capture the effects of the nonlinearities. However, the computational cost associated with these simulations is considerably higher compared to linear frequency domain (FD) methods. In this regard, the following work deals with the nonlinear analysis of an oscillating wave surge converter (OWSC) in the FD via the statistical linearization (SL) technique. Four nonlinearities for the proposed device are addressed: Coulomb-like torque regulated by the direction of motion, viscous drag torque, nonlinear buoyant net torque, and parametric excitation torque modulated by the flap angle. The reliability of the SL technique is compared with nonlinear TD simulations in terms of response probability distribution and power spectrum density (PSD) of the response and torque; and mean power produced. The results have demonstrated a good agreement between TD simulations and SL, while the computation time of the SL model is approximately 3 orders of magnitude faster. As a result, SL is a valuable tool to assess the OWSC performance under various wave scenarios over a range of design parameters, and can assist the development of such wave energy converters (WECs).

Stochastic Dynamic Analysis of U-OWC Wave Energy Converters

2017 ◽  
Author(s):  
Pol D. Spanos ◽  
Federica M. Strati ◽  
Giovanni Malara ◽  
Felice Arena
Keyword(s):  
Monte Carlo ◽  
Wave Energy ◽  
Random Vibration ◽  
Equations Of Motion ◽  
Statistical Linearization ◽  
Stochastic Dynamic ◽  
Sea Waves ◽  
Monte Carlo Data ◽  
Linear Differential ◽  
Stochastic Dynamic Analysis

The paper presents a random vibration analysis of a U-Oscillating Water Column wave energy harvester (U-OWC). The U-OWC comprises a vertical duct on the wave beaten side, in addition to the elements of conventional OWCs. From a mathematical perspective, the U-OWC dynamic response is governed by a set of coupled non-linear differential equations with asymmetric matrices of mass, damping, and stiffness. In this work, an approximate analytical solution of the U-OWC equations of motion is sought by using the technique of statistical linearization. This technique allows pursuing rapid random vibration analyses via classical linear input-output relationships. The analysis is conducted by considering the case of the full-scale prototype in the port of Civitavecchia (Rome, Italy). The reliability of the proposed approach is assessed versus relevant Monte Carlo data. For this, realizations of sea states compatible with typical power spectral density functions of sea waves are employed. The performed analyses prove that the statistical linearization technique based approach is an efficient and reliable tool which may both circumvent the use of time-consuming Monte Carlo simulations, and be used for a variety of design optimization related parameter studies.

Bayesian Estimation of DSGE Models

2015 ◽  
Author(s):  
Edward P. Herbst ◽  
Frank Schorfheide
Keyword(s):  
Monte Carlo ◽  
Sequential Monte Carlo ◽  
Likelihood Function ◽  
Academic Research ◽  
Dynamic Stochastic General Equilibrium ◽  
Computational Techniques ◽  
Dsge Models ◽  
Monte Carlo Techniques ◽  
Dynamic Stochastic ◽  
Theoretical Foundations

Dynamic stochastic general equilibrium (DSGE) models have become one of the workhorses of modern macroeconomics and are extensively used for academic research as well as forecasting and policy analysis at central banks. This book introduces readers to state-of-the-art computational techniques used in the Bayesian analysis of DSGE models. The book covers Markov chain Monte Carlo techniques for linearized DSGE models, novel sequential Monte Carlo methods that can be used for parameter inference, and the estimation of nonlinear DSGE models based on particle filter approximations of the likelihood function. The theoretical foundations of the algorithms are discussed in depth, and detailed empirical applications and numerical illustrations are provided. The book also gives invaluable advice on how to tailor these algorithms to specific applications and assess the accuracy and reliability of the computations. The book is essential reading for graduate students, academic researchers, and practitioners at policy institutions.

Neutron dose evaluation of Elekta Linac at two energies (10 & 18 MV) by MCNP code and comparison with experimental measurements

2014 ◽  
Vol 6 (1) ◽  
pp. 1006-1015
Author(s):  
Negin Shagholi ◽  
Hassan Ali ◽  
Mahdi Sadeghi ◽  
Arjang Shahvar ◽  
Hoda Darestani ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Measurement Data ◽  
Calculated Data ◽  
High Energy ◽  
Neutron Dose ◽  
Dose Assessment ◽  
Photon Flux ◽  
Dose Equivalent ◽  
Monte Carlo Techniques ◽  
Neutron Dose Equivalent

Medical linear accelerators, besides the clinically high energy electron and photon beams, produce other secondary particles such as neutrons which escalate the delivered dose. In this study the neutron dose at 10 and 18MV Elekta linac was obtained by using TLD600 and TLD700 as well as Monte Carlo simulation. For neutron dose assessment in 2020 cm2 field, TLDs were calibrated at first. Gamma calibration was performed with 10 and 18 MV linac and neutron calibration was done with 241Am-Be neutron source. For simulation, MCNPX code was used then calculated neutron dose equivalent was compared with measurement data. Neutron dose equivalent at 18 MV was measured by using TLDs on the phantom surface and depths of 1, 2, 3.3, 4, 5 and 6 cm. Neutron dose at depths of less than 3.3cm was zero and maximized at the depth of 4 cm (44.39 mSvGy-1), whereas calculation resulted  in the maximum of 2.32 mSvGy-1 at the same depth. Neutron dose at 10 MV was measured by using TLDs on the phantom surface and depths of 1, 2, 2.5, 3.3, 4 and 5 cm. No photoneutron dose was observed at depths of less than 3.3cm and the maximum was at 4cm equal to 5.44mSvGy-1, however, the calculated data showed the maximum of 0.077mSvGy-1 at the same depth. The comparison between measured photo neutron dose and calculated data along the beam axis in different depths, shows that the measurement data were much more than the calculated data, so it seems that TLD600 and TLD700 pairs are not suitable dosimeters for neutron dosimetry in linac central axis due to high photon flux, whereas MCNPX Monte Carlo techniques still remain a valuable tool for photonuclear dose studies.

scholarly journals Stochastic Order and Generalized Weighted Mean Invariance

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 662
Author(s):  
Mateu Sbert ◽  
Jordi Poch ◽  
Shuning Chen ◽  
Víctor Elvira
Keyword(s):  
Monte Carlo ◽  
Probability Distributions ◽  
Stochastic Order ◽  
Arithmetic Mean ◽  
Stochastic Orders ◽  
Arithmetic Means ◽  
Increasing Convex Order ◽  
Monte Carlo Techniques ◽  
Multiple Importance Sampling ◽  
Invariance Properties

In this paper, we present order invariance theoretical results for weighted quasi-arithmetic means of a monotonic series of numbers. The quasi-arithmetic mean, or Kolmogorov–Nagumo mean, generalizes the classical mean and appears in many disciplines, from information theory to physics, from economics to traffic flow. Stochastic orders are defined on weights (or equivalently, discrete probability distributions). They were introduced to study risk in economics and decision theory, and recently have found utility in Monte Carlo techniques and in image processing. We show in this paper that, if two distributions of weights are ordered under first stochastic order, then for any monotonic series of numbers their weighted quasi-arithmetic means share the same order. This means for instance that arithmetic and harmonic mean for two different distributions of weights always have to be aligned if the weights are stochastically ordered, this is, either both means increase or both decrease. We explore the invariance properties when convex (concave) functions define both the quasi-arithmetic mean and the series of numbers, we show its relationship with increasing concave order and increasing convex order, and we observe the important role played by a new defined mirror property of stochastic orders. We also give some applications to entropy and cross-entropy and present an example of multiple importance sampling Monte Carlo technique that illustrates the usefulness and transversality of our approach. Invariance theorems are useful when a system is represented by a set of quasi-arithmetic means and we want to change the distribution of weights so that all means evolve in the same direction.

scholarly journals Random Sampling Many-Dimensional Sets Arising in Control

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 580
Author(s):  
Pavel Shcherbakov ◽  
Mingyue Ding ◽  
Ming Yuchi
Keyword(s):  
Monte Carlo ◽  
Random Sampling ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Computational Mathematics ◽  
Closed Form Solutions ◽  
Monte Carlo Techniques ◽  
Control Optimization ◽  
Point Representation ◽  
Hit And Run

Various Monte Carlo techniques for random point generation over sets of interest are widely used in many areas of computational mathematics, optimization, data processing, etc. Whereas for regularly shaped sets such sampling is immediate to arrange, for nontrivial, implicitly specified domains these techniques are not easy to implement. We consider the so-called Hit-and-Run algorithm, a representative of the class of Markov chain Monte Carlo methods, which became popular in recent years. To perform random sampling over a set, this method requires only the knowledge of the intersection of a line through a point inside the set with the boundary of this set. This component of the Hit-and-Run procedure, known as boundary oracle, has to be performed quickly when applied to economy point representation of many-dimensional sets within the randomized approach to data mining, image reconstruction, control, optimization, etc. In this paper, we consider several vector and matrix sets typically encountered in control and specified by linear matrix inequalities. Closed-form solutions are proposed for finding the respective points of intersection, leading to efficient boundary oracles; they are generalized to robust formulations where the system matrices contain norm-bounded uncertainty.

Multilevel Monte Carlo by using the Halton sequence

2020 ◽  
Vol 26 (3) ◽  
pp. 193-203
Author(s):  
Shady Ahmed Nagy ◽  
Mohamed A. El-Beltagy ◽  
Mohamed Wafa
Keyword(s):  
Monte Carlo ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Computational Cost ◽  
Random Numbers ◽  
Multilevel Monte Carlo ◽  
Halton Sequence ◽  
Random Generator ◽  
Mc Simulation ◽  
Multilevel Monte Carlo Method

AbstractMonte Carlo (MC) simulation depends on pseudo-random numbers. The generation of these numbers is examined in connection with the Brownian motion. We present the low discrepancy sequence known as Halton sequence that generates different stochastic samples in an equally distributed form. This will increase the convergence and accuracy using the generated different samples in the Multilevel Monte Carlo method (MLMC). We compare algorithms by using a pseudo-random generator and a random generator depending on a Halton sequence. The computational cost for different stochastic differential equations increases in a standard MC technique. It will be highly reduced using a Halton sequence, especially in multiplicative stochastic differential equations.

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