Numerical test for single concrete armour layer on breakwaters

2016 ◽  
Vol 169 (4) ◽  
pp. 174-187 ◽  
Author(s):  
Eleni Anastasaki ◽  
John-Paul Latham ◽  
Jiansheng Xiang
Keyword(s):  
Numerical Test

scholarly journals Convergence results for an averaged LQR problem with applications to reinforcement learning

2021 ◽  
Author(s):  
Andrea Pesare ◽  
Michele Palladino ◽  
Maurizio Falcone
Keyword(s):  
Optimal Control ◽  
Reinforcement Learning ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Current System ◽  
Numerical Test ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Lqr Problem ◽  
Quadratic Optimal Control

AbstractIn this paper, we will deal with a linear quadratic optimal control problem with unknown dynamics. As a modeling assumption, we will suppose that the knowledge that an agent has on the current system is represented by a probability distribution $$\pi $$ π on the space of matrices. Furthermore, we will assume that such a probability measure is opportunely updated to take into account the increased experience that the agent obtains while exploring the environment, approximating with increasing accuracy the underlying dynamics. Under these assumptions, we will show that the optimal control obtained by solving the “average” linear quadratic optimal control problem with respect to a certain $$\pi $$ π converges to the optimal control driven related to the linear quadratic optimal control problem governed by the actual, underlying dynamics. This approach is closely related to model-based reinforcement learning algorithms where prior and posterior probability distributions describing the knowledge on the uncertain system are recursively updated. In the last section, we will show a numerical test that confirms the theoretical results.

Autonomous Vehicles’ Car-Following Drivability Evaluation Based on Driving Behavior Spectrum Reference Model

2021 ◽  
pp. 036119812199485
Author(s):  
Xiao Qi ◽  
Ying Ni ◽  
Yiming Xu ◽  
Ye Tian ◽  
Junhua Wang ◽  
...  
Keyword(s):  
Autonomous Vehicles ◽  
Reference Model ◽  
Numerical Test ◽  
Safety Evaluation ◽  
Driving Behavior ◽  
Car Following ◽  
Driving Behaviors ◽  
Human Driver ◽  
Normal Human ◽  
Naturalistic Driving

A large portion of the accidents involving autonomous vehicles (AVs) are not caused by the functionality of AV, but rather because of human intervention, since AVs’ driving behavior was not properly understood by human drivers. Such misunderstanding leads to dangerous situations during interaction between AV and human-driven vehicle (HV). However, few researches considered HV-AV interaction safety in AV safety evaluation processes. One of the solutions is to let AV mimic a normal HV’s driving behavior so as to avoid misunderstanding to the most extent. Therefore, to evaluate the differences of driving behaviors between existing AV and HV is necessary. DRIVABILITY is defined in this study to characterize the similarity between AV’s driving behaviors and expected behaviors by human drivers. A driving behavior spectrum reference model built based on human drivers’ behaviors is proposed to evaluate AVs’ car-following drivability. The indicator of the desired reaction time (DRT) is proposed to characterize the car-following drivability. Relative entropy between the DRT distribution of AV and that of the entire human driver population are used to quantify the differences between driving behaviors. A human driver behavior spectrum was configured based on naturalistic driving data by human drivers collected in Shanghai, China. It is observed in the numerical test that amongst all three types of preset AVs in the well-received simulation package VTD, the brisk AV emulates a normal human driver to the most extent (ranking at 55th percentile), while the default AV and the comfortable AV rank at 35th and 8th percentile, respectively.

scholarly journals Identification of coexisting dynamics in boundary layer flows through proper orthogonal decomposition with weighting matrices

Meccanica ◽  
2021 ◽  
Author(s):  
Matteo Dellacasagrande ◽  
Dario Barsi ◽  
Patrizia Bagnerini ◽  
Davide Lengani ◽  
Daniele Simoni
Keyword(s):  
Experimental Data ◽  
Proper Orthogonal Decomposition ◽  
Fourier Transforms ◽  
Free Stream ◽  
Numerical Test ◽  
Separated Flow ◽  
Orthogonal Decomposition ◽  
Inner Product ◽  
Test Case ◽  
Proper Orthogonal

AbstractA different version of the classic proper orthogonal decomposition (POD) procedure introducing spatial and temporal weighting matrices is proposed. Furthermore, a newly defined non-Euclidean (NE) inner product that retain similarities with the POD is introduced in the paper. The aim is to emphasize fluctuation events localized in spatio-temporal regions with low kinetic energy magnitude, which are not highlighted by the classic POD. The different variants proposed in this work are applied to numerical and experimental data, highlighting analogies and differences with respect to the classic and other normalized variants of POD available in the literature. The numerical test case provides a noise-free environment of the strongly organized vortex shedding behind a cylinder. Conversely, experimental data describing transitional boundary layers are used to test the capability of the procedures in strongly not uniform flows. By-pass and separated flow transition processes developing with high free-stream disturbances have been considered. In both cases streaky structures are expected to interact with other vortical structures (i.e. free-stream vortices in the by-pass case and Kelvin–Helmholtz rolls in the separated type) that carry a significant different amount of energy. Modes obtained by the non-Euclidean POD (NE-POD) procedure (where weighted projections are considered) are shown to better extract low energy events sparse in time and space with respect to modes extracted by other variants. Moreover, NE-POD modes are further decomposed as a combination of Fourier transforms of the related temporal coefficients and the normalized data ensemble to isolate the frequency content of each mode.

scholarly journals Finding Global Minima with a Filled Function Approach for Non-Smooth Global Optimization

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Weixiang Wang ◽  
Youlin Shang ◽  
Ying Zhang
Keyword(s):  
Global Optimization ◽  
Optimization Problem ◽  
Numerical Test ◽  
Function Approach ◽  
Global Optimization Problem ◽  
Computational Results ◽  
Filled Function ◽  
Global Minima ◽  
Smooth Case ◽  
Definition Of

A filled function approach is proposed for solving a non-smooth unconstrained global optimization problem. First, the definition of filled function in Zhang (2009) for smooth global optimization is extended to non-smooth case and a new one is put forwarded. Then, a novel filled function is proposed for non-smooth the global optimization and a corresponding non-smooth algorithm based on the filled function is designed. At last, a numerical test is made. The computational results demonstrate that the proposed approach is effcient and reliable.

scholarly journals A posteriori error estimates for a multi-scale finite-element method

2021 ◽  
Vol 40 (4) ◽  
Author(s):  
Khallih Ahmed Blal ◽  
Brahim Allam ◽  
Zoubida Mghazli
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
A Posteriori Error Estimates ◽  
Numerical Test ◽  
Posteriori Error ◽  
Diffusion Problem ◽  
A Posteriori ◽  
Essential Information ◽  
Multi Scale ◽  
Element Method

AbstractWe are interested in the discretization of a diffusion problem with highly oscillating coefficient, by a multi-scale finite-element method (MsFEM). The objective of this method is to capture the multi-scale structure of the solution via local basis functions which contain the essential information on small scales. In this paper, we perform an a posteriori analysis of this discretization. The main result consists of building error indicators with respect to both small and large meshes used in this method. We present a numerical test in which the experiments are in good coherency with the results of analysis.

scholarly journals Multiobjective Optimization Model for Collaborative En-Route and Slot Allocation

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Shangwen Yang ◽  
Jingting Zhang ◽  
Ping Chen ◽  
Yongjie Yan
Keyword(s):  
Decision Making ◽  
Traffic Control ◽  
Programming Model ◽  
Numerical Test ◽  
Simulated Data ◽  
Slot Allocation ◽  
Collaborative Decision Making ◽  
Average Delay ◽  
Flight Delay ◽  
Collaborative Decision

To allocate the en-routes and slots resource to the flights with collaborative decision-making, a multiobjective 0-1 integer programming model was proposed. According to different demands from air traffic control departments, airlines, and passengers, efficiency, equity, and effectiveness principles of collaborative decision-making were considered. With the aim to minimize the total flight delay costs, the total number of turning points, and average delay time of passengers, the effectiveness constraints were achieved. The algorithm was designed to solve the model on the basis of the objective method, and Lingo11 and MatlabR2007b were applied in numerical tests. To test how well the model works in real world, a numerical test was performed based on the simulated data of a civil en-route. Test results show that, compared with the traditional strategy of first come first served, the model gains better effect. The superiority of the model was verified.

The Numerical Analysis and Simulation of a Linearized Crank-Nicolson H1-GMFEM for Nonlinear Coupled BBM Equations

2014 ◽  
Vol 513-517 ◽  
pp. 1919-1926 ◽  
Author(s):  
Min Zhang ◽  
Zu Deng Yu ◽  
Yang Liu ◽  
Hong Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Scheme ◽  
Mixed Finite Element ◽  
A Priori ◽  
Numerical Test ◽  
Mixed Finite Element Method ◽  
Spatial Direction ◽  
Time Direction ◽  
Crank Nicolson

In this article, the numerical scheme of a linearized Crank-Nicolson (C-N) method based on H1-Galerkin mixed finite element method (H1-GMFEM) is studied and analyzed for nonlinear coupled BBM equations. In this method, the spatial direction is approximated by an H1-GMFEM and the time direction is discretized by a linearized Crank-Nicolson method. Some optimal a priori error results are derived for four important variables. For conforming the theoretical analysis, a numerical test is presented.

A TWELFTH-ORDER FOUR-STEP FORMULA FOR THE NUMERICAL INTEGRATION OF THE ONE-DIMENSIONAL SCHRÖDINGER EQUATION

2003 ◽  
Vol 14 (08) ◽  
pp. 1087-1105 ◽  
Author(s):  
ZHONGCHENG WANG ◽  
YONGMING DAI
Keyword(s):  
Schrödinger Equation ◽  
Numerical Integration ◽  
Schrodinger Equation ◽  
Numerical Test ◽  
New Method ◽  
Step Method ◽  
One Dimensional ◽  
The Stability ◽  
The One ◽  
Order Four

A new twelfth-order four-step formula containing fourth derivatives for the numerical integration of the one-dimensional Schrödinger equation has been developed. It was found that by adding multi-derivative terms, the stability of a linear multi-step method can be improved and the interval of periodicity of this new method is larger than that of the Numerov's method. The numerical test shows that the new method is superior to the previous lower orders in both accuracy and efficiency and it is specially applied to the problem when an increasing accuracy is requested.

scholarly journals A derivative free globally convergent method and its deformations

2021 ◽  
Author(s):  
Manoj Kumar Singh ◽  
Arvind K. Singh
Keyword(s):  
Difference Operator ◽  
Linear Equations ◽  
Numerical Test ◽  
Test Functions ◽  
Globally Convergent ◽  
Forward Difference ◽  
Derivative Free ◽  
Fractal Patterns ◽  
Convergent Method ◽  
Non Linear Equations

AbstractThe motive of the present work is to introduce and investigate the quadratically convergent Newton’s like method for solving the non-linear equations. We have studied some new properties of a Newton’s like method with examples and obtained a derivative-free globally convergent Newton’s like method using forward difference operator and bisection method. Finally, we have used various numerical test functions along with their fractal patterns to show the utility of the proposed method. These patterns support the numerical results and explain the compactness regarding the convergence, divergence and stability of the methods to different roots.

scholarly journals Numerical test of disk trial wave function for a half-filled Landau level

2000 ◽  
Vol 62 (12) ◽  
pp. 8171-8179 ◽  
Author(s):  
S.-R. Eric Yang ◽  
Min-Chul Cha ◽  
Jung Hoon Han
Keyword(s):  
Wave Function ◽  
Landau Level ◽  
Numerical Test ◽  
Trial Wave Function
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