scholarly journals Application of Cell Mapping methods to a discontinuous dynamic system

1994 ◽  
Vol 6 (1) ◽  
pp. 87-99 ◽  
Author(s):  
J. A. W. Van Der Spek ◽  
C. A. L. De Hoon ◽  
A. De Kraker ◽  
D. H. Van Campen
Keyword(s):  
Dynamic System ◽  
Cell Mapping ◽  
Cell Mapping Methods

An efficient parallel implementation of cell mapping methods for MDOF systems

2016 ◽  
Vol 86 (4) ◽  
pp. 2279-2290 ◽  
Author(s):  
Pierpaolo Belardinelli ◽  
Stefano Lenci
Keyword(s):  
Parallel Implementation ◽  
Cell Mapping ◽  
Cell Mapping Methods ◽  
Mdof Systems

A Cell Mapping Method for Nonlinear Deterministic and Stochastic Systems—Part I: The Method of Analysis

1986 ◽  
Vol 53 (3) ◽  
pp. 695-701 ◽  
Author(s):  
C. S. Hsu ◽  
H. M. Chiu
Keyword(s):  
Stochastic Systems ◽  
Mapping Method ◽  
Cell Mapping ◽  
Generalized Cell Mapping ◽  
Strongly Nonlinear ◽  
Cell Mapping Methods ◽  
The Past ◽  
Simple Cell Mapping ◽  
A Cell ◽  
Vibration Problems

In the past few years as an attempt to devise more efficient and more practical ways of determining the global behavior of strongly nonlinear systems, two cell-to-cell mapping methods have been proposed, namely, the simple cell mapping and the generalized cell mapping. In this first part of the two-part paper we present a different and more efficient cell mapping method for treating nonlinear vibration problems. The vibratory systems may be deterministic or stochastic. The method utilizes compatible simple and generalized cell mapping and it combines the advantages of both. Applications to various systems will be presented in the second part of the paper.

scholarly journals Diagnosis of an Alternator System Using Quantized Approaches

2020 ◽  
Vol 6 (2) ◽  
Author(s):  
Sara Mohon ◽  
Pierluigi Pisu
Keyword(s):  
Fault Detection ◽  
Linear System ◽  
Reference Voltage ◽  
Fault Detection And Isolation ◽  
Stochastic Method ◽  
Cell Mapping ◽  
Generalized Cell Mapping ◽  
Cell Mapping Methods

In this paper, the Generalized Cell Mapping (GCM) method for a linear system is compared with a new stochastic method for novel cell-to-cell mapping. The authors presented the new stochastic method in Mohon and Pisu (2013). The two methods are compared in an application example of a vehicle alternator. The alternator may experience three faults including belt slippage, a faulty diode connection, or incorrect controller reference voltage. Fault detection and isolation (FDI) is performed using the two cell-to-cell mapping methods. The results show that the new stochastic method is slower but yields better isolation results than the GCM method.

Cell Mapping Methods

2019 ◽  
Author(s):  
Jian-Qiao Sun ◽  
Fu-Rui Xiong ◽  
Oliver Schütze ◽  
Carlos Hernández
Keyword(s):  
Cell Mapping ◽  
Cell Mapping Methods

Parallel Cell Mapping Method for Global Analysis of High-Dimensional Nonlinear Dynamical Systems1

2015 ◽  
Vol 82 (11) ◽  
Author(s):  
Fu-Rui Xiong ◽  
Zhi-Chang Qin ◽  
Qian Ding ◽  
Carlos Hernández ◽  
Jesús Fernandez ◽  
...  
Keyword(s):  
Steady State ◽  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Global Analysis ◽  
Mapping Method ◽  
Cell Mapping ◽  
Nonlinear Dynamical ◽  
Cell Mapping Methods ◽  
Steady State Responses ◽  
State Responses

The cell mapping methods were originated by Hsu in 1980s for global analysis of nonlinear dynamical systems that can have multiple steady-state responses including equilibrium states, periodic motions, and chaotic attractors. The cell mapping methods have been applied to deterministic, stochastic, and fuzzy dynamical systems. Two important extensions of the cell mapping method have been developed to improve the accuracy of the solutions obtained in the cell state space: the interpolated cell mapping (ICM) and the set-oriented method with subdivision technique. For a long time, the cell mapping methods have been applied to dynamical systems with low dimension until now. With the advent of cheap dynamic memory and massively parallel computing technologies, such as the graphical processing units (GPUs), global analysis of moderate- to high-dimensional nonlinear dynamical systems becomes feasible. This paper presents a parallel cell mapping method for global analysis of nonlinear dynamical systems. The simple cell mapping (SCM) and generalized cell mapping (GCM) are implemented in a hybrid manner. The solution process starts with a coarse cell partition to obtain a covering set of the steady-state responses, followed by the subdivision technique to enhance the accuracy of the steady-state responses. When the cells are small enough, no further subdivision is necessary. We propose to treat the solutions obtained by the cell mapping method on a sufficiently fine grid as a database, which provides a basis for the ICM to generate the pointwise approximation of the solutions without additional numerical integrations of differential equations. A modified global analysis of nonlinear systems with transient states is developed by taking advantage of parallel computing without subdivision. To validate the parallelized cell mapping techniques and to demonstrate the effectiveness of the proposed method, a low-dimensional dynamical system governed by implicit mappings is first presented, followed by the global analysis of a three-dimensional plasma model and a six-dimensional Lorenz system. For the six-dimensional example, an error analysis of the ICM is conducted with the Hausdorff distance as a metric.

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