Modeling Parametric Uncertainty Using Polynomial Chaos Theory

2019 ◽  
Vol 3 (27) ◽  
pp. 243-256 ◽  
Author(s):  
Shriram Santhanagopalan ◽  
Ralph E. White
Keyword(s):  
Chaos Theory ◽  
Polynomial Chaos ◽  
Parametric Uncertainty ◽  
Polynomial Chaos Theory

Automating the Derivation of the Equations of Motion of a Multibody Dynamic System With Uncertainty Using Polynomial Chaos Theory and Variational Work

2019 ◽  
Vol 15 (1) ◽  
Author(s):  
Paul S. Ryan ◽  
Sarah C. Baxter ◽  
Philip A. Voglewede
Keyword(s):  
Chaos Theory ◽  
Polynomial Chaos ◽  
Equations Of Motion ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Multibody Dynamic ◽  
Mass Spring ◽  
Polynomial Chaos Theory ◽  
Multibody Dynamic System ◽  
Crank Mechanism

Abstract Understanding how variation impacts a multibody dynamic (MBD) system's response is important to ensure the robustness of a system. However, how the variation propagates into the MBD system is complicated because MBD systems are typically governed by a system of large differential algebraic equations. This paper presents a novel process, variational work, along with the polynomial chaos multibody dynamics (PCMBoD) automation process for utilizing polynomial chaos theory (PCT) in the analysis of uncertainties in an MBD system. Variational work allows the complexity of the traditional PCT approach to be reduced. With variational work and the constrained Lagrangian formulation, the equations of motion of an MBD PCT system can be constructed using the PCMBoD automated process. To demonstrate the PCMBoD process, two examples, a mass-spring-damper and a two link slider–crank mechanism, are shown.

Battery State of Health and Charge Estimation Using Polynomial Chaos Theory

2013 ◽  
Author(s):  
Saeid Bashash ◽  
Hosam K. Fathy
Keyword(s):  
Parameter Estimation ◽  
Chaos Theory ◽  
Polynomial Chaos ◽  
Search Algorithm ◽  
Estimation Method ◽  
Experimental Tests ◽  
Internal Resistance ◽  
Battery State Of Charge ◽  
Gradient Based ◽  
Polynomial Chaos Theory

In this effort, we use the generalized Polynomial Chaos theory (gPC) for the real-time state and parameter estimation of electrochemical batteries. We use an equivalent circuit battery model, comprising two states and five parameters, and formulate the online parameter estimation problem using battery current and voltage measurements. Using a combination of the conventional recursive gradient-based search algorithm and gPC framework, we propose a novel battery parameter estimation strategy capable of estimating both battery state-of-charge (SOC) and parameters related to battery health, e.g., battery charge capacity, internal resistance, and relaxation time constant. Using a combination of experimental tests and numerical simulations, we examine and demonstrate the effectiveness of the proposed battery estimation method.

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