Simulating Univariate and Multivariate Tukey g-and-h Distributions Based on the Method of Percentiles

This paper derives closed-form solutions for the g-and-h shape parameters associated with the Tukey family of distributions based on the method of percentiles (MOP). A proposed MOP univariate procedure is described and compared with the method of moments (MOM) in the context of distribution fitting and estimating skew and kurtosis functions. The MOP methodology is also extended from univariate to multivariate data generation. A procedure is described for simulating nonnormal distributions with specified Spearman correlations. The MOP procedure has an advantage over the MOM because it does not require numerical integration to compute intermediate correlations. Simulation results demonstrate that the proposed MOP procedure is superior to the MOM in terms of distribution fitting, estimation, relative bias, and relative error.

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Modeling perforates in mufflers using two-ports

Journal of Vibration and Acoustics ◽

10.1115/1.4001510 ◽

2010 ◽

Vol 132 (6) ◽

Cited By ~ 23

Author(s):

T. Elnady ◽

M. Åbom ◽

S. Allam

Keyword(s):

Closed Form ◽

Closed Form Solutions ◽

Analysis Techniques ◽

Segmentation Approach ◽

Simulation Results ◽

Number Of Segments ◽

Good Agreement

One of the main sources of noise of a vehicle is the engine where its noise is usually damped by means of acoustic mufflers. A very common problem in the modeling of automotive mufflers is that of two flow ducts coupled through a perforate. A new segmentation approach is developed here based on two-port analysis techniques, in order to model perforated pipes using general two-port codes, which are widely available. Examples are given for simple muffler configurations and the convergence of the technique is investigated based on the number of segments used. The results are compared with closed form solutions form the literature. Finally, an analysis of a complicated multichamber perforated muffler system is presented. The two-port simulation results show good agreement with both the measurements, and the simulations using the classical four-port elements.

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A NEW CLOSED FORM SOLUTION FOR DYNAMIC STABILITY ANALYSIS OF ROLLING AIRFRAMES HAVING ONE PAIR ON-OFF ACTUATOR

Aviation ◽

10.3846/aviation.2021.13832 ◽

2021 ◽

Vol 25 (2) ◽

pp. 92-103

Author(s):

Jalal Karimi

Keyword(s):

Stability Analysis ◽

Closed Form ◽

Dynamic Stability ◽

Linear Theory ◽

Closed Form Solution ◽

Form Solution ◽

Control Surface ◽

Closed Form Solutions ◽

Forcing Term ◽

Simulation Results

In this paper, the dynamic stability analysis of a rolling airframe actuated by one pair ON-OFF actuator using linear theory is presented via developing a new closed form solution. The effect of discontinuous forcing term on rolling airframe stability is studied. In contrast to tricyclic motion with constant forcing term (constant non-homogeneous term) in which only the amplitude of nutation and precession is affected, it is found that ON-OFF control affects both amplitude and phase of nutation and precession motions. In the case of discontinuous control surface, there are two sources for resonance instability. Finally, through simulation results of closed form solutions, a comparison between airframe’ response to ideal and real ON-OFF command is achieved. The effect of ON-OFF control on angular motion is also evaluated.

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