scholarly journals An improved closed-form solution to interfacial stresses in plated beams using a two-stage approach

2010 ◽  
Vol 52 (1) ◽  
pp. 13-30 ◽  
Author(s):  
Jian Yang ◽  
Jianqiao Ye
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Two Stage ◽  
Interfacial Stresses

scholarly journals Mean square cross error: performance analysis and applications in non-Gaussian signal processing

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yunxiang Zhang ◽  
Yuyang Zhao ◽  
Gang Wang ◽  
Rui Xue
Keyword(s):  
Performance Analysis ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Mean Square ◽  
Error Signal ◽  
Two Stage ◽  
Information Theoretic Learning ◽  
The Mean ◽  
Maximum Correntropy Criterion

AbstractMost of the cost functions of adaptive filtering algorithms include the square error, which depends on the current error signal. When the additive noise is impulsive, we can expect that the square error will be very large. By contrast, the cross error, which is the correlation of the error signal and its delay, may be very small. Based on this fact, we propose a new cost function called the mean square cross error for adaptive filters, and provide the mean value and mean square performance analysis in detail. Furthermore, we present a two-stage method to estimate the closed-form solutions for the proposed method, and generalize the two-stage method to estimate the closed-form solution of the information theoretic learning methods, including least mean fourth, maximum correntropy criterion, generalized maximum correntropy criterion, and minimum kernel risk-sensitive loss. The simulations of the adaptive solutions and closed-form solution show the effectivity of the new method.

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

scholarly journals A Closed-Form Solution to Planar Feature-Based Registration of LiDAR Point Clouds

2021 ◽  
Vol 10 (7) ◽  
pp. 435
Author(s):  
Yongbo Wang ◽  
Nanshan Zheng ◽  
Zhengfu Bian
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Simulated Data ◽  
Real Data ◽  
Point Clouds ◽  
Form Solution ◽  
Spatial Transformation ◽  
Dual Quaternions ◽  
Feature Based ◽  
Planar Feature

Since pairwise registration is a necessary step for the seamless fusion of point clouds from neighboring stations, a closed-form solution to planar feature-based registration of LiDAR (Light Detection and Ranging) point clouds is proposed in this paper. Based on the Plücker coordinate-based representation of linear features in three-dimensional space, a quad tuple-based representation of planar features is introduced, which makes it possible to directly determine the difference between any two planar features. Dual quaternions are employed to represent spatial transformation and operations between dual quaternions and the quad tuple-based representation of planar features are given, with which an error norm is constructed. Based on L2-norm-minimization, detailed derivations of the proposed solution are explained step by step. Two experiments were designed in which simulated data and real data were both used to verify the correctness and the feasibility of the proposed solution. With the simulated data, the calculated registration results were consistent with the pre-established parameters, which verifies the correctness of the presented solution. With the real data, the calculated registration results were consistent with the results calculated by iterative methods. Conclusions can be drawn from the two experiments: (1) The proposed solution does not require any initial estimates of the unknown parameters in advance, which assures the stability and robustness of the solution; (2) Using dual quaternions to represent spatial transformation greatly reduces the additional constraints in the estimation process.

Sign in / Sign up

Export Citation Format

Share Document