On the Evaluation of Correction Terms of Gaussian Integration

2011 ◽  
Vol 13 (1) ◽  
pp. 58-61 ◽  
Author(s):  
Mohankumar Nandagopal
Keyword(s):  
Gaussian Integration ◽  
Correction Terms

Embedding non-linear filtering in autonomous underwater vehicle dynamics via the Kolmogorov backward equation

2021 ◽  
pp. 014233122110196
Author(s):  
Ravish H. Hirpara ◽  
Shambhu N. Sharma
Keyword(s):  
State Vector ◽  
Autonomous Underwater Vehicle ◽  
Underwater Vehicle ◽  
Linear Filtering ◽  
Homogeneous Markov Process ◽  
Non Linear ◽  
Backward Equation ◽  
Noise Correction ◽  
Ito Process ◽  
Correction Terms

This paper revisits the state vector of an autonomous underwater vehicle (AUV) dynamics coupled with the underwater Markovian stochasticity in the ‘non-linear filtering’ context. The underwater stochasticity is attributed to atmospheric turbulence, planetary interactions, sea surface conditions and astronomical phenomena. In this paper, we adopt the Itô process, a homogeneous Markov process, to describe the AUV state vector evolution equation. This paper accounts for the process noise as well as observation noise correction terms by considering the underwater filtering model. The non-linear filtering of the paper is achieved using the Kolmogorov backward equation and the evolution of the conditional characteristic function. The non-linear filtering equation is the cornerstone formalism of stochastic optimal control systems. Most notably, this paper introduces the non-linear filtering theory into an underwater vehicle stochastic system by constructing a lemma and a theorem for the underwater vehicle stochastic differential equation that were not available in the literature.

scholarly journals TOWARD AN IMPROVED EMPIRICAL FORMULA FOR LONGSHORE SAND TRANSPORT

1988 ◽  
Vol 1 (21) ◽  
pp. 88 ◽  
Author(s):  
Nicholas C. Kraus ◽  
Kathryn J. Gingerich ◽  
Julie Dean Rosati
Keyword(s):  
Oscillatory Flow ◽  
Field Experiments ◽  
Surf Zone ◽  
Transport Rate ◽  
Sand Transport ◽  
Longshore Current ◽  
Wave Energy Dissipation ◽  
Total Transport ◽  
Local Wave ◽  
Correction Terms

This paper presents results of two field experiments performed using portable traps to obtain point measurements of the longshore sand transport rate in the surf zone. The magnitude of the transport rate per unit width of surf zone is found to depend on the product of the local wave height and mean longshore current speed, but correlation is much improved by including two correction terms, one accounting for local wave energy dissipation and the other for the fluctuation in the longshore current. The field transport rates are also found to be compatible with laboratory rates obtained under combined unidirectional and oscillatory flow. Total transport rates previously reported for this experiment program are revised with recently determined sand trapping efficiencies.

Corrected diffusion approximations in certain random walk problems

1979 ◽  
Vol 11 (4) ◽  
pp. 701-719 ◽  
Author(s):  
D. Siegmund
Keyword(s):  
Random Walk ◽  
Diffusion Approximation ◽  
Diffusion Approximations ◽  
Infinite Time ◽  
Ladder Height ◽  
Correction Terms

Correction terms are obtained for the diffusion approximation to one- and two-barrier ruin problems in finite and infinite time. The corrections involve moments of ladder-height distributions, and a method is given for calculating them numerically. Examples show that the corrected approximations can be much more accurate than the originals.

Generalized information and entanglement entropy, gravitation and holography

2015 ◽  
Vol 30 (16) ◽  
pp. 1530039 ◽  
Author(s):  
O. Obregón
Keyword(s):  
Entanglement Entropy ◽  
Ideal Gas ◽  
Einstein Equations ◽  
Von Neumann Entropy ◽  
Nonextensive Statistical Mechanics ◽  
Von Neumann ◽  
H Theorem ◽  
Gauge Gravity ◽  
Gravity Duality ◽  
Correction Terms

A nonextensive statistical mechanics entropy that depends only on the probability distribution is proposed in the framework of superstatistics. It is based on a Γ(χ2) distribution that depends on β and also on pl. The corresponding modified von Neumann entropy is constructed; it is shown that it can also be obtained from a generalized Replica trick. We further demonstrate a generalized H-theorem. Considering the entropy as a function of the temperature and volume, it is possible to generalize the equation of state of an ideal gas. Moreover, following the entropic force formulation a generalized Newton's law is obtained, and following the proposal that the Einstein equations can be deduced from the Clausius law, we discuss on the structure that a generalized Einstein's theory would have. Lastly, we address the question whether the generalized entanglement entropy can play a role in the gauge/gravity duality. We pay attention to 2d CFT and their gravity duals. The correction terms to the von Neumann entropy result more relevant than the usual UV ones and also than those due to the area dependent AdS3 entropy which result comparable to the UV ones. Then the correction terms due to the new entropy would modify the Ryu–Takayanagi identification between the CFT entanglement entropy and the AdS entropy in a different manner than the UV ones or than the corrections to the AdS3 area dependent entropy.

An inhomogeneous cell-based smoothed finite element method for the nonlinear transient response of functionally graded magneto-electro-elastic structures with damping factors

2018 ◽  
Vol 30 (3) ◽  
pp. 416-437 ◽  
Author(s):  
Liming Zhou ◽  
Ming Li ◽  
Bingkun Chen ◽  
Feng Li ◽  
Xiaolin Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Element Model ◽  
Micro Electro Mechanical System ◽  
Functionally Graded ◽  
Elastic Structures ◽  
Mapping Procedure ◽  
Gaussian Integration ◽  
Smoothed Finite Element Method ◽  
Element Method

In this article, an inhomogeneous cell-based smoothed finite element method (ICS-FEM) was proposed to overcome the over-stiffness of finite element method in calculating transient responses of functionally graded magneto-electro-elastic structures. The ICS-FEM equations were derived by introducing gradient smoothing technique into the standard finite element model; a close-to-exact system stiffness was also obtained. In addition, ICS-FEM could be carried out with user-defined sub-routines in the business software now available conveniently. In ICS-FEM, the parameters at Gaussian integration point were adopted directly in the creation of shape functions; the computation process is simplified, for the mapping procedure in standard finite element method is not required; this also gives permission to utilize poor quality elements and few mesh distortions during large deformation. Combining with the improved Newmark scheme, several numerical examples were used to prove the accuracy, convergence, and efficiency of ICS-FEM. Results showed that ICS-FEM could provide solutions with higher accuracy and reliability than finite element method in analyzing models with Rayleigh damping. Such method is also applied to complex structures such as typical micro-electro-mechanical system–based functionally graded magneto-electro-elastic energy harvester. Hence, ICS-FEM can be a powerful tool for transient problems of functionally graded magneto-electro-elastic models with damping which is of great value in designing intelligence structures.

scholarly journals Empirical correction techniques: analysis and applications to chaotically driven low-order atmospheric models

2013 ◽  
Vol 20 (2) ◽  
pp. 199-206
Author(s):  
I. Trpevski ◽  
L. Basnarkov ◽  
D. Smilkov ◽  
L. Kocarev
Keyword(s):  
Linear Regression Method ◽  
Atmospheric Models ◽  
Time Intervals ◽  
Average Value ◽  
Climate Forecasting ◽  
Empirical Correction ◽  
Weather And Climate ◽  
Real World Applications ◽  
Correction Terms ◽  
Low Order

Abstract. Contemporary tools for reducing model error in weather and climate forecasting models include empirical correction techniques. In this paper we explore the use of such techniques on low-order atmospheric models. We first present an iterative linear regression method for model correction that works efficiently when the reference truth is sampled at large time intervals, which is typical for real world applications. Furthermore we investigate two recently proposed empirical correction techniques on Lorenz models with constant forcing while the reference truth is given by a Lorenz system driven with chaotic forcing. Both methods indicate that the largest increase in predictability comes from correction terms that are close to the average value of the chaotic forcing.

scholarly journals High gain observers with updated gain and homogeneous correction terms

Automatica ◽  
2009 ◽  
Vol 45 (2) ◽  
pp. 422-428 ◽  
Author(s):  
V. Andrieu ◽  
L. Praly ◽  
A. Astolfi
Keyword(s):  
High Gain ◽  
Correction Terms

A New Heat Transfer Correlation for Supercritical RP-3 Flowing in Vertical Tubes

2017 ◽  
Author(s):  
Longyun Wang ◽  
Zhi Tao ◽  
Jianqin Zhu ◽  
Haiwang Li ◽  
Zeyuan Cheng
Keyword(s):  
Heat Transfer ◽  
Influence Factors ◽  
Hydrocarbon Fuel ◽  
Operating Conditions ◽  
Major Influence ◽  
Absolute Deviation ◽  
New Correlation ◽  
Vertical Tubes ◽  
Correction Terms ◽  
Good Agreement

A new empirical correlation for upward flowing supercritical aviation kerosene RP-3 in the vertical tubes is proposed. In order to obtain the database, numerical simulation with a four-component surrogate model on RP-3 and LS low Reynolds turbulence model in vertical circular tube has been performed. Tubes of diameter 2mm to 10mm are studied and operating conditions cover pressure from 3MPa to 6MPa. Heat flux is 500KW/m2, mass flow rate is 700kg/(m2·s). The numerical results on wall temperature distribution under various conditions are compared with experimental data and a good agreement is achieved. The existing correlations are summarized and classified into three categories. Three representative correlations of each category are selected out to evaluate the applicability in heat transfer of supercritical RP-3. The result shows that correlations concluded from water and carbon-dioxide do not perform well in predicting heat transfer of hydrocarbon fuel. The mean absolute deviation of them is up to 20% and predict about 80% of the entire database within 30% error bands. So a new correlation which is applicable to different working conditions for supercritical RP-3 is put forward. Gnielinski type has been adapted as the basis of the new correlation for its higher accuracy. In consideration of major influence factors of supercritical heat transfer, correction terms of density and buoyancy effect are added in. The new correlation has a MAD of 9.26%, predicting 90.6% of the entire database within ±15% error bands. The comparisons validate the applicability of the new correlation.

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