scholarly journals Solve thermal explosion model by central difference and Newton iteration method

10.19139/135 ◽  
2015 ◽  
Vol 3 (2) ◽  
Author(s):  
Xijian Wang ◽  
Tonghua Zeng
Keyword(s):  
Thermal Explosion ◽  
Iteration Method ◽  
Newton Iteration ◽  
Central Difference ◽  
Newton Iteration Method ◽  
Thermal Explosion Model

scholarly journals Statistical Process Monitoring with Biogeography-Based Optimization Independent Component Analysis

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Xiangshun Li ◽  
Di Wei ◽  
Cheng Lei ◽  
Zhiang Li ◽  
Wenlin Wang
Keyword(s):  
Fault Detection ◽  
Independent Component Analysis ◽  
Process Monitoring ◽  
Iteration Method ◽  
Newton Iteration ◽  
Independent Component ◽  
Statistical Process ◽  
Independent Components ◽  
Newton Iteration Method ◽  
Statistical Process Monitoring

Independent Component Analysis (ICA), a type of typical data-driven fault detection techniques, has been widely applied for monitoring industrial processes. FastICA is a classical algorithm of ICA, which extracts independent components by using the Newton iteration method. However, the choice of the initial iterative point of Newton iteration method is difficult; sometimes, selection of different initial iterative points tends to show completely different effects for fault detection. So far, there is still no good strategy to get an ideal initial iterative point for ICA. To solve this problem, a modified ICA algorithm based on biogeography-based optimization (BBO) called BBO-ICA is proposed for the purpose of multivariate statistical process monitoring. The Newton iteration method is replaced with BBO here for extracting independent components. BBO is a novel and effective optimization method to search extremes or maximums. Comparing with the traditional intelligent optimization algorithm of particle swarm optimization (PSO) and so on, BBO behaves with stronger capability and accuracy of searching for solution space. Moreover, numerical simulations are finished with the platform of DAMADICS. Results demonstrate the practicability and effectiveness of BBO-ICA. The proposed BBO-ICA shows better performance of process monitoring than FastICA and PSO-ICA for DAMADICS.

scholarly journals A family of modified Newton iteration method for solving nonlinear algebraic equations

2017 ◽  
Vol 20 (K2) ◽  
pp. 34-41
Author(s):  
Luc Xuan Nghiem ◽  
Hieu Nhu Nguyen
Keyword(s):  
Iteration Method ◽  
Order Of Convergence ◽  
Approximate Solutions ◽  
Newton Iteration ◽  
Convergence Order ◽  
Correction Function ◽  
Algebraic Equations ◽  
Order Condition ◽  
Nonlinear Algebraic Equations ◽  
Newton Iteration Method

In this study, a modified Newton iteration version for solving nonlinear algebraic equations is formulated using a correction function derived from convergence order condition of iteration. If the second order of convergence is selected, we get a family of the modified Newton iteration method. Several forms of the correction function are proposed in checking the effectiveness and accuracy of the present iteration method. For illustration, approximate solutions of four examples of nonlinear algebraic equations are obtained and then compared with those obtained from the classical Newton iteration method.

Linear Complementary Equation Method Applied in the Load Response of Cable-Strut Systems

1998 ◽  
Vol 13 (1) ◽  
pp. 35-40 ◽  
Author(s):  
B-B. Wang ◽  
S-Z. Xu ◽  
X-L. Liu
Keyword(s):  
Iteration Method ◽  
Step Length ◽  
Newton Iteration ◽  
Load Response ◽  
Computation Process ◽  
Novel Method ◽  
Newton Iteration Method ◽  
Complementary Equation ◽  
The Given ◽  
Derivation Process

In this paper, the drawbacks of the Newton iteration method are analyzed. Then the Linear Complementary Equation (LCE) method is introduced into the cable-strut system to cope with the “retiring” problem of elements under load. The corresponding variants of the function of zero-stress and the flow factor of zero-stress are invented to represent the characteristics of cables and struts retiring from functioning. The derivation process is given in detail and its efficiency is proved by case studies. The LCE method has overcome all the drawbacks of the iteration method, because its computation process is non-conditionally stable, and its step length can be determined at about 1/5 of the given load value for all cases to ensure accuracy. It is novel method for studying the load response of cable-strut systems.

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