Information Theoretic Causality Measures for System Identification of Mechanical Systems

[+] Author and Article Information
Jared Elinger

Georgia Tech, Department of Mechanical Engineering

Jonathan Rogers

Georgia Tech, Department of Mechanical Engineering

1Corresponding author.

ASME doi:10.1115/1.4040253 History: Received October 03, 2017; Revised May 02, 2018


Parameter estimation and model order reduction (MOR) are important system identification techniques used in the development of models for mechanical systems. A variety of classical parameter estimation and MOR methods are available for nonlinear systems but performance generally suffers when little is known about the system model a priori. Recent advancements in information theory have yielded a quantity called causation entropy, which is a measure of influence between elements in a multivariate time series. In parameter estimation problems involving dynamic systems, causation entropy can be used to identify which state transition functions in a discrete-time model are important in driving the system dynamics, leading to reductions in the dimensionality of the parameter space. This method can likewise be used in black box system identification problems to reduce model order and limit issues with overfitting. Building on previous work, this paper illustrates the use of causation entropy-enabled parameter estimation for nonlinear mechanical systems of varying complexity. Furthermore, an extension to black-box system identification is proposed wherein causation entropy is used to identify the proper model order of parameterized black-box models. This technique is illustrated using nonlinear differential equation (NDE) models of physical devices, including a nonlinear spring-mass-damper, a pendulum, and a nonlinear model of a car suspension. Overall, results show that causation entropy is a promising new tool for both gray-box and black-box system identification that can speed convergence toward a parameter solution and mitigate problems with model overfitting.

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