random simplex
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Mathematika ◽  
2011 ◽  
Vol 58 (1) ◽  
pp. 77-91 ◽  
Author(s):  
Luis Rademacher
Keyword(s):  

Author(s):  
M. Faggioni ◽  
F. Pellicano ◽  
A. Andrisano ◽  
G. Bertacchi

This paper presents a global optimization method able to find gear profile modifications that minimize vibrations. A non linear dynamic model is used to study the vibrational behavior; the dynamic model is validated using data available in literature. The optimization method takes into account the influence of torque levels both on the static and the dynamic response. Therefore, two different objective functions are considered; the first one is based on static analysis and the second one is based on the dynamic behavior of a lumped mass system. The procedure can find the optimal profile modification that reduce the vibrations over a wide range of operating conditions. In order to reduce the computational cost, a Random-Simplex optimization algorithm is developed; the optimum reliability is also estimated using a Monte Carlo simulation. The approach shows good performances both for the computational efficiency and the reliability of results.


1995 ◽  
Vol 56 (2) ◽  
pp. 79-81 ◽  
Author(s):  
Andrei Z. Broder ◽  
Martin E. Dyer ◽  
Alan M. Frieze ◽  
Prabhakar Raghavan ◽  
Eli Upfal

1991 ◽  
Vol 32 (10) ◽  
pp. 1143-1153 ◽  
Author(s):  
Zhou Qingchu ◽  
Xu Naixin ◽  
Shih Shengtai

1984 ◽  
Vol 21 (03) ◽  
pp. 651-653
Author(s):  
John Gates

This note shows how the initial density of the volume of a random simplex in a body, K, depends upon the fourth moment of sectional area and so rejects the conjecture that this initial density is independent of K.


1984 ◽  
Vol 21 (3) ◽  
pp. 651-653 ◽  
Author(s):  
John Gates

This note shows how the initial density of the volume of a random simplex in a body, K, depends upon the fourth moment of sectional area and so rejects the conjecture that this initial density is independent of K.


1977 ◽  
Vol 14 (3) ◽  
pp. 647-653 ◽  
Author(s):  
Harold Ruben

A proof is given of a conjecture in the literature of geometrical probability that the r-content of the r-simplex whose r + 1 vertices are independent random points of which p are uniform in the interior and q uniform on the boundary of a unit n-ball (1 ≦ r ≦ n; 0 ≦ p, q ≦ r + 1, p + q = r + 1) is asymptotically normal (n →∞) with asymptotic mean and variance and , respectively.


1977 ◽  
Vol 14 (03) ◽  
pp. 647-653 ◽  
Author(s):  
Harold Ruben

A proof is given of a conjecture in the literature of geometrical probability that the r-content of the r-simplex whose r + 1 vertices are independent random points of which p are uniform in the interior and q uniform on the boundary of a unit n-ball (1 ≦ r ≦ n; 0 ≦ p, q ≦ r + 1, p + q = r + 1) is asymptotically normal (n →∞) with asymptotic mean and variance and , respectively.


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