scholarly journals Software Sensors for Nonlinear Dynamical Systems

2020 ◽  
Vol 3 ◽  
pp. xviii-xviii
Author(s):  
Driss Boutat
Keyword(s):  
Dynamic Models ◽  
Nonlinear Dynamical Systems ◽  
Real Life ◽  
System Structure ◽  
Accurate Estimation ◽  
Nonlinear Dynamical ◽  
Physical Measurements ◽  
Physical Sensors ◽  
Software Sensors ◽  
System Data

Modelling a real life system starts with defining its inputs/outputs, where the inputs depend on the nature of the actuator (or to take actions) and the outputs are measurements. In general, some of the outputs are measured using physical sensors, while the unavailable states can be obtained using the so-called software sensors (or observers). For accurate understanding real life system, data about its state are usually measured using physical sensors. This can be expensive and makes the system structure cumbersome. Besides, in many cases, it is simply impossible to measure some system information directly. Due to these drawbacks, a solution may be the introduction of the so-called software sensors or observers. These sensors are based on a well- defined system model and provide an accurate estimation of the missing data from the available physical measurements. Actually, obtaining a well-defined mathematical model is not always possible, or the obtained models do not allow obtaining strategies to drive accurate comprehensive conclusion of our system. Therefore, how we can to overcome those difficulties? Using dynamic models learning.

Constraint optimization of nonlinear McPherson suspension system using genetic algorithm and ADAMS software

2021 ◽  
pp. 107754632110260
Author(s):  
Arash Vahedi ◽  
Ali Jamali
Keyword(s):  
Genetic Algorithm ◽  
Nonlinear Dynamical Systems ◽  
Real Life ◽  
Suspension System ◽  
Building Structures ◽  
Nonlinear Dynamical ◽  
Camber Angle ◽  
Design Variables ◽  
Adams Software ◽  
Actual Size

In this article, optimization of the McPherson suspension mechanism of a real car named Arisan is considered. In this regard, a model based on a real-life suspension system is proposed with the least simplification. This model is built in the ADAMS/View software based on the actual size of the suspension mechanism of Arisan. Moreover, the user-written code of the genetic algorithm in C is added as a plug-in to the ADAMS/View software in a completely innovative way to optimize the suspension system. 16 parameters of the suspension system are selected as design variables to wholly handle its geometry. The value of all design variables is optimally found by GA to minimize the variation of the camber angle as an objective function. Comparison of the obtained optimum suspension by the proposed method with the actual suspension system of Arisan shows a 23.5% improvement in the camber variation angle. It is worth noting that the proposed method does not require a mathematical model of the suspension system that leads to some simplifications such as linearization and non-friction joints. The proposed method can be used for modeling and optimization of other nonlinear dynamical systems such as robotics and building structures.

Linear and Nonlinear Dynamic Behaviour

2018 ◽  
Author(s):  
Ray Huffaker ◽  
Marco Bittelli ◽  
Rodolfo Rosa
Keyword(s):  
Dynamic Behavior ◽  
Dynamic Systems ◽  
Dynamic Behaviour ◽  
Nonlinear Dynamical Systems ◽  
Logistic Map ◽  
Nonlinear Dynamical ◽  
Deterministic Dynamic ◽  
Random Behavior ◽  
Single Solution ◽  
Equivalent Systems

In this chapter, we describe how highly erratic dynamic behavior can arise from a nonlinear logistic map, and how this apparently random behavior is governed by a surprising order. With this lesson in mind, we should not be overly surprised that highly erratic and random appearing observed data might also be generated by parsimonious deterministic dynamic systems. At a minimum, we contend that researchers should apply NLTS to test for this possibility. We also introduced tools to analyze dynamic behavior that form the foundation for NLTS. In particular, we have stressed the quite unexpected capability to achieve some form of predictability even with only one trajectory at hand. In subsequent chapters, we treat known nonlinear dynamical systems as unknown, and investigate how NLTS methods rely on a single solution (or multiple solutions) generated by them to reconstruct equivalent systems. This is a conventional approach in the literature for seeing how NLTS methods work since we know what needs to be reconstructed.

scholarly journals Analysis of Stochastic Generation and Shifts of Phantom Attractors in a Climate–Vegetation Dynamical Model

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1329
Author(s):  
Lev Ryashko ◽  
Dmitri V. Alexandrov ◽  
Irina Bashkirtseva
Keyword(s):  
Multiplicative Noise ◽  
Nonlinear Dynamical Systems ◽  
Stochastic Theory ◽  
Slow Variable ◽  
Theoretical Description ◽  
Mathematical Study ◽  
Stochastic Generation ◽  
Nonlinear Dynamical ◽  
Additive And Multiplicative Noise ◽  
And Shifts

A problem of the noise-induced generation and shifts of phantom attractors in nonlinear dynamical systems is considered. On the basis of the model describing interaction of the climate and vegetation we study the probabilistic mechanisms of noise-induced systematic shifts in global temperature both upward (“warming”) and downward (“freezing”). These shifts are associated with changes in the area of Earth covered by vegetation. The mathematical study of these noise-induced phenomena is performed within the framework of the stochastic theory of phantom attractors in slow-fast systems. We give a theoretical description of stochastic generation and shifts of phantom attractors based on the method of freezing a slow variable and averaging a fast one. The probabilistic mechanisms of oppositely directed shifts caused by additive and multiplicative noise are discussed.

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