Bayesian Forecasting of Dynamic Extreme Quantiles

Forecasting ◽  
2021 ◽  
Vol 3 (4) ◽  
pp. 729-740
Author(s):  
Douglas E. Johnston
Keyword(s):  
Structural Engineering ◽  
State Space Model ◽  
Predictive Distribution ◽  
Value Theory ◽  
Computationally Efficient ◽  
Unknown Parameters ◽  
Time Step ◽  
Extreme Quantile ◽  
Recursive Solution ◽  
Probability Densities

In this paper, we provide a novel Bayesian solution to forecasting extreme quantile thresholds that are dynamic in nature. This is an important problem in many fields of study including climatology, structural engineering, and finance. We utilize results from extreme value theory to provide the backdrop for developing a state-space model for the unknown parameters of the observed time-series. To solve for the requisite probability densities, we derive a Rao-Blackwellized particle filter and, most importantly, a computationally efficient, recursive solution. Using the filter, the predictive distribution of future observations, conditioned on the past data, is forecast at each time-step and used to compute extreme quantile levels. We illustrate the improvement in forecasting ability, versus traditional methods, using simulations and also apply our technique to financial market data.

scholarly journals A Computationally Efficient Shallow Water Model for Mixed Cohesive and Non-Cohesive Sediment Transport in the Yangtze Estuary

Water ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1435
Author(s):  
Peng Hu ◽  
Junyu Tao ◽  
Aofei Ji ◽  
Wei Li ◽  
Zhiguo He
Keyword(s):  
Sediment Transport ◽  
Yangtze Estuary ◽  
Water Model ◽  
Cohesive Sediments ◽  
Shallow Water Model ◽  
Computationally Efficient ◽  
Time Step ◽  
The Yangtze Estuary ◽  
Erosion Coefficient ◽  
Cohesive Sediment Transport

In this paper, a computationally efficient shallow water model is developed for sediment transport in the Yangtze estuary by considering mixed cohesive and non-cohesive sediment transport. It is firstly shown that the model is capable of reproducing tidal-hydrodynamics in the estuarine region. Secondly, it is demonstrated that the observed temporal variation of suspended sediment concentration (SSC) for mixed cohesive and non-cohesive sediments can be well-captured by the model with calibrated parameters (i.e., critical shear stresses for erosion/deposition, erosion coefficient). Numerical comparative studies indicate that: (1) consideration of multiple sediment fraction (both cohesive and non-cohesive sediments) is important for accurate modeling of SSC in the Yangtze Estuary; (2) the critical shear stress and the erosion coefficient is shown to be site-dependent, for which intensive calibration may be required; and (3) the Deepwater Navigation Channel (DNC) project may lead to enhanced current velocity and thus reduced sediment deposition in the North Passage of the Yangtze Estuary. Finally, the implementation of the hybrid local time step/global maximum time step (LTS/GMaTS) (using LTS to update the hydro-sediment module but using GMaTS to update the morphodynamic module) can lead to a reduction of as high as 90% in the computational cost for the Yangtze Estuary. This advantage, along with its well-demonstrated quantitative accuracy, indicates that the present model should find wide applications in estuarine regions.

Motion Response Control of the DWSC Spar Based on State-Space Model

2012 ◽  
Author(s):  
Xiaochuan Yu ◽  
Jeffrey Falzarano
Keyword(s):  
State Space ◽  
Transfer Functions ◽  
State Space Model ◽  
Development Program ◽  
Naval Research ◽  
Hydrodynamic Coefficients ◽  
Time Step ◽  
Response Control ◽  
Motion Response ◽  
Space Model

In 2007, the Office of Naval Research (ONR) started a technology development program called STLVAST (Small to Large Vessel At-Sea Transfer), in order to develop ‘enabling capabilities’ in the realm of logistic transfer (i.e. stores, equipment, vehicles) between a large transport vessel and a smaller T-craft ship, using a Deep Water Stable Crane (DWSC) spar between them. In this paper, the equation of motions of the single DWSC spar is initially expressed as the standard state-space model. Then the ODE solver of Matlab is directly employed to obtain the motion responses at each time step. Two levels of approximation of hydrodynamic coefficients are considered in this study. One is the Constant Coefficient Method (CCM), and the other one is the Impulse Response Function (IRF) method, with fluid memory effects considered. WAMIT software is used to calculate the hydrodynamic coefficients, including the added mass, radiation damping, IRF, the first order and second order waves loads transfer functions, etc. The motion response control is achieved by assuming the thrusters can provide the optimal feedback force derived from Linear Quadratic Regulator (LQR) method.

Newmark-Beta Method in Discrete Elastic Rods Algorithm to Avoid Energy Dissipation

2019 ◽  
Vol 86 (8) ◽  
Author(s):  
Weicheng Huang ◽  
Mohammad Khalid Jawed
Keyword(s):  
Energy Dissipation ◽  
Time Integration ◽  
Integration Scheme ◽  
Integration Step ◽  
Elastic Rods ◽  
Computationally Efficient ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Time Integration Scheme

Discrete elastic rods (DER) algorithm presents a computationally efficient means of simulating the geometrically nonlinear dynamics of elastic rods. However, it can suffer from artificial energy loss during the time integration step. Our approach extends the existing DER technique by using a different time integration scheme—we consider a second-order, implicit Newmark-beta method to avoid energy dissipation. This treatment shows better convergence with time step size, specially when the damping forces are negligible and the structure undergoes vibratory motion. Two demonstrations—a cantilever beam and a helical rod hanging under gravity—are used to show the effectiveness of the modified discrete elastic rods simulator.

scholarly journals Computationally efficient methods for modelling laser wakefield acceleration in the blowout regime

2012 ◽  
Vol 78 (4) ◽  
pp. 469-482 ◽  
Author(s):  
B. M. COWAN ◽  
S. Y. KALMYKOV ◽  
A. BECK ◽  
X. DAVOINE ◽  
K. BUNKERS ◽  
...  
Keyword(s):  
Initial Conditions ◽  
Cylindrical Symmetry ◽  
Small Time ◽  
Numerical Dispersion ◽  
Computationally Efficient ◽  
Plasma Bubble ◽  
Time Step ◽  
Simulation Code ◽  
Particle In Cell ◽  
Comput Phys

AbstractElectron self-injection and acceleration until dephasing in the blowout regime is studied for a set of initial conditions typical of recent experiments with 100-terawatt-class lasers. Two different approaches to computationally efficient, fully explicit, 3D particle-in-cell modelling are examined. First, the Cartesian code vorpal (Nieter, C. and Cary, J. R. 2004 VORPAL: a versatile plasma simulation code. J. Comput. Phys.196, 538) using a perfect-dispersion electromagnetic solver precisely describes the laser pulse and bubble dynamics, taking advantage of coarser resolution in the propagation direction, with a proportionally larger time step. Using third-order splines for macroparticles helps suppress the sampling noise while keeping the usage of computational resources modest. The second way to reduce the simulation load is using reduced-geometry codes. In our case, the quasi-cylindrical code calder-circ (Lifschitz, A. F. et al. 2009 Particle-in-cell modelling of laser-plasma interaction using Fourier decomposition. J. Comput. Phys.228(5), 1803–1814) uses decomposition of fields and currents into a set of poloidal modes, while the macroparticles move in the Cartesian 3D space. Cylindrical symmetry of the interaction allows using just two modes, reducing the computational load to roughly that of a planar Cartesian simulation while preserving the 3D nature of the interaction. This significant economy of resources allows using fine resolution in the direction of propagation and a small time step, making numerical dispersion vanishingly small, together with a large number of particles per cell, enabling good particle statistics. Quantitative agreement of two simulations indicates that these are free of numerical artefacts. Both approaches thus retrieve the physically correct evolution of the plasma bubble, recovering the intrinsic connection of electron self-injection to the nonlinear optical evolution of the driver.

scholarly journals Accelerated Runge-Kutta Methods

2008 ◽  
Vol 2008 ◽  
pp. 1-38 ◽  
Author(s):  
Firdaus E. Udwadia ◽  
Artin Farahani
Keyword(s):  
Computationally Efficient ◽  
Step Size ◽  
Time Step ◽  
Integration Schemes ◽  
Local Accuracy ◽  
Numerical Integrators ◽  
One Step ◽  
Runge Kutta ◽  
Finite Step ◽  
Proof Of Convergence

Standard Runge-Kutta methods are explicit, one-step, and generally constant step-size numerical integrators for the solution of initial value problems. Such integration schemes of orders 3, 4, and 5 require 3, 4, and 6 function evaluations per time step of integration, respectively. In this paper, we propose a set of simple, explicit, and constant step-size Accerelated-Runge-Kutta methods that are two-step in nature. For orders 3, 4, and 5, they require only 2, 3, and 5 function evaluations per time step, respectively. Therefore, they are more computationally efficient at achieving the same order of local accuracy. We present here the derivation and optimization of these accelerated integration methods. We include the proof of convergence and stability under certain conditions as well as stability regions for finite step sizes. Several numerical examples are provided to illustrate the accuracy, stability, and efficiency of the proposed methods in comparison with standard Runge-Kutta methods.

Studies on the Accuracy Stability and Efficiency of a New Time Integration Scheme for Ballast Modeling Using the Discrete Element Method

2014 ◽  
Author(s):  
G. F. Mathews ◽  
R. L. Mullen ◽  
D. C. Rizos
Keyword(s):  
Particle Interaction ◽  
Time Integration ◽  
Discrete Element ◽  
Critical Discussion ◽  
Implicit Time ◽  
Integration Scheme ◽  
Computationally Efficient ◽  
Time Step ◽  
Central Difference ◽  
Time Integration Scheme

This paper presents the development of a semi-implicit time integration scheme, originally developed for structural dynamics in the 1970’s, and its implementation for use in Discrete Element Methods (DEM) for rigid particle interaction, and interaction of elastic bodies that are modeled as a cluster of rigid interconnected particles. The method is developed in view of ballast modeling that accounts for the flexibility of aggregates and the arbitrary shape and size of granules. The proposed scheme does not require any matrix inversions and is expressed in an incremental form making it appropriate for non-linear problems. The proposed method focuses on improving the efficiency, stability and accuracy of the solutions, as compared to current practice. A critical discussion of the findings of the studies is presented. Extended verification and assessment studies demonstrate that the proposed algorithm is unconditionally stable and accurate even for large time step sizes. It is demonstrated that the proposed method is at least as computationally efficient as the Central Difference Method. Guidelines for the implementation of the method to ballast modeling are discussed.

DYNAMIC ANALYSIS OF FRAMES WITH MATERIAL AND GEOMETRIC NONLINEARITIES BASED ON THE SEMIRIGID TECHNIQUE

2008 ◽  
Vol 08 (03) ◽  
pp. 415-438 ◽  
Author(s):  
F. T. K. AU ◽  
Z. H. YAN
Keyword(s):  
Dynamic Analysis ◽  
Stiffness Matrix ◽  
Plastic Hinge ◽  
Nonlinear Dynamic Analysis ◽  
Yield Condition ◽  
Computationally Efficient ◽  
Time Step ◽  
Geometric Nonlinearities ◽  
Frame Element ◽  
Sum Of Products

This paper presents a method for nonlinear dynamic analysis of frames with material and geometric nonlinearities which is based on the semirigid technique. The plastic hinge that accounts for the material nonlinearity is modeled as a pseudo-semirigid connection with nonlinear hysteretic moment-curvature characteristics at the element ends. The stiffness matrix of a frame element with material and geometric nonlinearities is expressed as the sum of products of the standard stiffness matrix and the geometric stiffness matrix of the element, with their corresponding correction matrices based on the plasticity factors developed from the section flexural stiffness at the plastic hinge locations. The combined stress yield condition is used for the force state determination of plastic hinges, and force equilibrium iterations and geometry updating for frames are carried out in every time step. When the key parameters of a structure are updated in a time step, the time step is split up into substeps to ensure accuracy while keeping the computations to a reasonable amount. The plastic rotation history can be calculated directly or in an approximate indirect way. The method is computationally efficient and it needs no additional connection elements, which makes it convenient for incorporation into existing linear dynamic analysis programs. Besides, the method can handle accurately and efficiently the dynamic analysis of nonlinear frames using relatively large time steps in conjunction with time step subdivision to cope with key parameter changes. A portal frame is used to verify the correctness of the proposed method. A more complicated five-story frame is used to illustrate the applicability and performance of the proposed method.

Modeling Arbitrarily Shaped Liquid Pipelines Using a Segmented Transmission Line Model

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Travis Wiens
Keyword(s):  
Transmission Line ◽  
Method Of Characteristics ◽  
Previous Method ◽  
New Method ◽  
Transmission Line Model ◽  
Computationally Efficient ◽  
Time Step ◽  
Line Model ◽  
Order Of Magnitude ◽  
Variable Time Step

Abstract This paper presents a new method of simulating the dynamic flow and pressure of laminar liquid flow through pipes of arbitrarily changing cross section. This method uses a segmented model based on the previously presented tapered transmission line model (TLM). This new method is computationally efficient and has comparable accuracy to previous methods such as the method of characteristics (MOC), but allow for more flexibility in solution time-step (such as accommodating variable time-step solvers), which is required if the rest of the system model has stiff equations. For the sample geometry presented, the new model calculates the dynamic response an order of magnitude faster than the previous method of characteristics solution, with minimal loss of accuracy.

scholarly journals Computationally Efficient Solution of a 2D Diffusive Wave Equation Used for Flood Inundation Problems

Water ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 2195 ◽  
Author(s):  
Wojciech Artichowicz ◽  
Dariusz Gąsiorowski
Keyword(s):  
Wave Equation ◽  
Parallel Implementation ◽  
Time Integration ◽  
Computational Time ◽  
System Of Nonlinear Equations ◽  
Computationally Efficient ◽  
Time Step ◽  
Finite Element Scheme ◽  
Numerical Errors ◽  
Floodplain Inundation

This paper presents a study dealing with increasing the computational efficiency in modeling floodplain inundation using a two-dimensional diffusive wave equation. To this end, the domain decomposition technique was used. The resulting one-dimensional diffusion equations were approximated in space with the modified finite element scheme, whereas time integration was carried out using the implicit two-level scheme. The proposed algorithm of the solution minimizes the numerical errors and is unconditionally stable. Consequently, it is possible to perform computations with a significantly greater time step than in the case of the explicit scheme. An additional efficiency improvement was achieved using the symmetry of the tridiagonal matrix of the arising system of nonlinear equations, due to the application of the parallelization strategy. The computational experiments showed that the proposed parallel implementation of the implicit scheme is very effective, at about two orders of magnitude with regard to computational time, in comparison with the explicit one.

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