Space–time model order reduction for nonlinear viscoelastic systems subjected to long-term loading

Meccanica ◽  
2017 ◽  
Vol 53 (6) ◽  
pp. 1333-1355 ◽  
Author(s):  
Felix Fritzen ◽  
Mohammadreza Hassani
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Space Time ◽  
Time Model ◽  
Model Order ◽  
Nonlinear Viscoelastic ◽  
Space Time Model

Long-term trends in ocean chlorophyll: update from a Bayesian hierarchical space-time model

2020 ◽  
Author(s):  
Claudie Beaulieu ◽  
Matthew Hammond ◽  
Stephanie Henson ◽  
Sujit Sahu
Keyword(s):  
Climate Change ◽  
Coupled Model ◽  
Climate Change Impacts ◽  
Space Time ◽  
Time Model ◽  
Bayesian Hierarchical ◽  
Color Sensors ◽  
Long Term Trends ◽  
Space Time Model

<p>Assessing ongoing changes in marine primary productivity is essential to determine the impacts of climate change on marine ecosystems and fisheries. Satellite ocean color sensors provide detailed coverage of ocean chlorophyll in space and time, now with a combined record length of just over 20 years. Detecting climate change impacts is hindered by the shortness of the record and the long timescale of memory within the ocean such that even the sign of change in ocean chlorophyll is still inconclusive from time-series analysis of satellite data. Here we use a Bayesian hierarchical space-time model to estimate long-term trends in ocean chlorophyll. The main advantage of this approach comes from the principle of ”borrowing strength” from neighboring grid cells in a given region to improve overall detection. We use coupled model simulations from the CMIP5 experiment to form priors to provide a “first guess” on observational trend estimates and their uncertainty that we then update using satellite observations. We compare the results with estimates obtained with the commonly used vague prior, reflecting the case where no independent knowledge is available.  A global average net positive chlorophyll trend is found, with stronger regional trends that are typically positive in high and mid latitudes, and negative at low latitudes outside the Atlantic. The Bayesian hierarchical model used here provides a framework for integrating different sources of data for detecting trends and estimating their uncertainty in studies of global change.</p>

Information Theoretic Tools for Parameter Estimation and Model Order Reduction for Mechanical Systems

2017 ◽  
Author(s):  
Jared D. Elinger ◽  
Jonathan D. Rogers
Keyword(s):  
Parameter Estimation ◽  
Nonlinear Systems ◽  
Model Order Reduction ◽  
Multivariate Time Series ◽  
A Priori ◽  
Order Reduction ◽  
Nonlinear Problems ◽  
Continuous Systems ◽  
Time Model ◽  
Model Order

Parameter estimation and model order reduction (MOR) are important techniques used in the development of mechanical system models. 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 the influence between multivariate time series. In parameter estimation problems involving dynamic systems, causation entropy can be used to identify which functions in a discrete-time model are important in driving the subsequent state values. This paper extends on previous works’ use of a Causation Entropy Matrix to nonlinear systems modeled from the real world. This work explores the conversion of continuous systems to a discrete model and applies the causation entropy matrix to the system. Results show that model structure can be estimated by the causation entropy matrix. This work extends the previous work by showing that the method can be applied to general nonlinear systems. Previously shown examples were toy, additively separable nonlinear problems. This work shows that the methodology can be extended to any nonlinear system, including time varying systems, which provides a framework to examine parameter estimation for general nonlinear systems.

scholarly journals Model Order Reduction: A Comparison between Integer and Non-Integer Order Systems Approaches

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 876 ◽  
Author(s):  
Riccardo Caponetto ◽  
José Tenreiro Machado ◽  
Emanuele Murgano ◽  
Maria Gabriella Xibilia
Keyword(s):  
Model Order Reduction ◽  
Control Strategies ◽  
Order Reduction ◽  
Open Loop ◽  
Long Term Memory ◽  
Fractional Order Systems ◽  
Model Order ◽  
Integer Order ◽  
Classical Control

In this paper, classical and non-integer model order reduction methodologies are compared. Non integer order calculus has been used to generalize many classical control strategies. The property of compressing information in modelling systems, distributed in time and space, and the capability of describing long-term memory effects in dynamical systems are two features suggesting also the application of fractional calculus in model order reduction. In the paper, an open loop balanced realization is compared with three approaches based on a non-integer representation of the reduced system. Several case studies are considered and compared. The results confirm the capability of fractional order systems to capture and compress the dynamics of high order systems.

THE NEW ALGORITHM OF SOLVING HARMONIC BALANCE EQUATIONS

2019 ◽  
Author(s):  
Vladimir Lantsov ◽  
A. Papulina
Keyword(s):  
Harmonic Balance ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Balance Equations ◽  
Model Order ◽  
Cad Systems ◽  
Computational Costs ◽  
Reduction Methods ◽  
Model Equations

The new algorithm of solving harmonic balance equations which used in electronic CAD systems is presented. The new algorithm is based on implementation to harmonic balance equations the ideas of model order reduction methods. This algorithm allows significantly reduce the size of memory for storing of model equations and reduce of computational costs.

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