On the spherical expansion for calculating the sound radiated by a baffled circular piston

2020 ◽  
pp. 2050026
Author(s):  
Jiaxin Zhong ◽  
Xiaojun Qiu
Keyword(s):  
Closed Form Solution ◽  
Accurate Method ◽  
Form Solution ◽  
Generalized Hypergeometric Functions ◽  
High Frequencies ◽  
Pressure Profiles ◽  
Spherical Expansion ◽  
Poor Convergence ◽  
Significant Figures ◽  
Recurrence Method

An efficient and accurate method for calculating the sound radiated by a baffled circular rigid piston is using spherical harmonics, and the solution is a series containing the integral of spherical Bessel functions. The integral is usually calculated with the generalized hypergeometric functions in existing literatures, which shows poor convergence at middle and high frequencies due to the overflow and the loss of significant figures. A rigorous and closed form solution of the integral is derived in this paper based on the recurrence method, which is accurate in the whole frequency range and thousands of times faster than the existing methods. It is shown that the proposed method can be extended for the calculation of the sound radiated by a baffled piston and an unbaffled resilient disk with axisymmetric velocity and pressure profiles, respectively, and some baffled rotating sources where the velocity profile is asymmetric.

scholarly journals Reconstruction of three-dimensional maps based on closed-form solutions of the variational problem of multisensor data registration

2019 ◽  
Vol 484 (6) ◽  
pp. 672-677
Author(s):  
A. V. Vokhmintcev ◽  
A. V. Melnikov ◽  
K. V. Mironov ◽  
V. V. Burlutskiy
Keyword(s):  
Closed Form ◽  
Large Scale ◽  
Three Dimensional ◽  
Dynamic Environment ◽  
Closed Form Solution ◽  
Point Clouds ◽  
Accurate Method ◽  
Form Solution ◽  
Closed Form Solutions ◽  
Reconstruction Methods

A closed-form solution is proposed for the problem of minimizing a functional consisting of two terms measuring mean-square distances for visually associated characteristic points on an image and meansquare distances for point clouds in terms of a point-to-plane metric. An accurate method for reconstructing three-dimensional dynamic environment is presented, and the properties of closed-form solutions are described. The proposed approach improves the accuracy and convergence of reconstruction methods for complex and large-scale scenes.

scholarly journals Wind energy forecasts in calculation of expected energy not served

2021 ◽  
Author(s):  
Richard Sun
Keyword(s):  
Markov Chain ◽  
Wind Energy ◽  
Optimal Power Flow ◽  
Markov Chain Model ◽  
Moving Average ◽  
Closed Form Solution ◽  
Arma Model ◽  
Accurate Method ◽  
Form Solution ◽  
Chain Model

The stochastic nature of wind energy generation introduces uncertainties and risk in generation schedules computed using optimal power flow (OPF). This risk is quantified as expected energy not served (EENS) and computed via an error distribution found for each hourly forecast. This thesis produces an accurate method of estimating EENS that is also suitable for real-time OPF calculation. This thesis examines two statistical predictive models used to forecast hourly production of wind energy generators (WEGs), Markov chain model, and auto-regressive moving-average (ARMA) model, and their effects on EENS. Persistence model is used as a benchmark for comparison. For persistence and ARMA models, both Gaussian and Cauchy error distributions are used to compute EENS via a closed-form solution that reduces computational complexity. Markov chain and ARMA both provide accurate forecasts of WEG power generation though Markov Chain model performs significantly better. The Markov chain model also produces the most accurate EENS estimate of the three models.

Solving the Robot-World/Hand-Eye Calibration Problem Using the Kronecker Product

2013 ◽  
Vol 5 (3) ◽  
Author(s):  
Mili Shah
Keyword(s):  
Kronecker Product ◽  
Closed Form Solution ◽  
Simulated Data ◽  
Real Data ◽  
Accurate Method ◽  
Form Solution ◽  
Singular Value ◽  
Error Metrics ◽  
Calibration Problem ◽  
Value Decomposition

This paper constructs a separable closed-form solution to the robot-world/hand-eye calibration problem AX = YB. Qualifications and properties that determine the uniqueness of X and Y as well as error metrics that measure the accuracy of a given X and Y are given. The formulation of the solution involves the Kronecker product and the singular value decomposition. The method is compared with existing solutions on simulated data and real data. It is shown that the Kronecker method that is presented in this paper is a reliable and accurate method for solving the robot-world/hand-eye calibration problem.

Piezoelectric Damping of Resistively Shunted Beams and Optimal Parameters for Maximum Damping

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Yabin Liao ◽  
Henry A. Sodano
Keyword(s):  
Optimal Parameter ◽  
Experimental Testing ◽  
Closed Form Solution ◽  
Electrical Energy ◽  
Accurate Method ◽  
Form Solution ◽  
Smart Structure ◽  
Complex Models ◽  
Shunt Damping ◽  
Determine System

This paper studies the piezoelectric damping of resistively shunted beams induced by the conversion of the vibration energy into electrical energy that is dissipated in the resistor through Joule heating. Significant contributions have been made in the modeling and development of the resistive shunt damping technique; however, many approaches involve complex models that require the use of numerical methods to determine system parameters and predict damping. This paper develops a closed-form solution for the optimal parameter of a resistive shunt damping system. The model is validated through experimental testing and provides a simple yet accurate method to predict the induced damping in a smart structure.

scholarly journals Wind energy forecasts in calculation of expected energy not served

2021 ◽  
Author(s):  
Richard Sun
Keyword(s):  
Markov Chain ◽  
Wind Energy ◽  
Optimal Power Flow ◽  
Markov Chain Model ◽  
Moving Average ◽  
Closed Form Solution ◽  
Arma Model ◽  
Accurate Method ◽  
Form Solution ◽  
Chain Model

The stochastic nature of wind energy generation introduces uncertainties and risk in generation schedules computed using optimal power flow (OPF). This risk is quantified as expected energy not served (EENS) and computed via an error distribution found for each hourly forecast. This thesis produces an accurate method of estimating EENS that is also suitable for real-time OPF calculation. This thesis examines two statistical predictive models used to forecast hourly production of wind energy generators (WEGs), Markov chain model, and auto-regressive moving-average (ARMA) model, and their effects on EENS. Persistence model is used as a benchmark for comparison. For persistence and ARMA models, both Gaussian and Cauchy error distributions are used to compute EENS via a closed-form solution that reduces computational complexity. Markov chain and ARMA both provide accurate forecasts of WEG power generation though Markov Chain model performs significantly better. The Markov chain model also produces the most accurate EENS estimate of the three models.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

Plane Wave Resonance in the Tire Air Cavity as a Vehicle Interior Noise Source

1995 ◽  
Vol 23 (1) ◽  
pp. 2-10 ◽  
Author(s):  
J. K. Thompson
Keyword(s):  
Closed Form Solution ◽  
Form Solution ◽  
Interior Noise ◽  
Cavity Resonance ◽  
Test Results ◽  
Vehicle Interior ◽  
Air Cavity ◽  
Vehicle Interior Noise ◽  
Wave Resonance ◽  
Resonance Frequencies

Abstract Vehicle interior noise is the result of numerous sources of excitation. One source involving tire pavement interaction is the tire air cavity resonance and the forcing it provides to the vehicle spindle: This paper applies fundamental principles combined with experimental verification to describe the tire cavity resonance. A closed form solution is developed to predict the resonance frequencies from geometric data. Tire test results are used to examine the accuracy of predictions of undeflected and deflected tire resonances. Errors in predicted and actual frequencies are shown to be less than 2%. The nature of the forcing this resonance as it applies to the vehicle spindle is also examined.

Capacity Analysis for Correlated Multi-Hop MIMO Channels under Colored Noise

2015 ◽  
Vol 1 ◽  
pp. 41
Author(s):  
Nguyen N. Tran ◽  
Ha X. Nguyen
Keyword(s):  
Computational Complexity ◽  
Mutual Information ◽  
Closed Form Solution ◽  
Optimal Solution ◽  
Form Solution ◽  
Maximization Problem ◽  
Capacity Analysis ◽  
Mimo Channels ◽  
Average Mutual Information ◽  
Channel Output

A capacity analysis for generally correlated wireless multi-hop multi-input multi-output (MIMO) channels is presented in this paper. The channel at each hop is spatially correlated, the source symbols are mutually correlated, and the additive Gaussian noises are colored. First, by invoking Karush-Kuhn-Tucker condition for the optimality of convex programming, we derive the optimal source symbol covariance for the maximum mutual information between the channel input and the channel output when having the full knowledge of channel at the transmitter. Secondly, we formulate the average mutual information maximization problem when having only the channel statistics at the transmitter. Since this problem is almost impossible to be solved analytically, the numerical interior-point-method is employed to obtain the optimal solution. Furthermore, to reduce the computational complexity, an asymptotic closed-form solution is derived by maximizing an upper bound of the objective function. Simulation results show that the average mutual information obtained by the asymptotic design is very closed to that obtained by the optimal design, while saving a huge computational complexity.

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