An error analysis of the dynamic mode decomposition

An error analysis of the dynamic mode decomposition Dynamic mode decomposition (DMD) is a new diagnostic technique in fluid mechanics which is growing in popularity. A powerful analysis tool, it has great potential for measuring the spatial and temporal dynamics of coherent structures in experimental fluid flows. To aid interpretation of experimental data, error-bars on the measured growth rates are needed. In this article, we undertake a massively parallel error analysis of the DMD algorithm using synthetic waveforms that are shown to be representative of the canonical instabilities observed in shear flows. We show that the waveform of the instability has a marked impact on the error of the measured growth rate. Sawtooth and square waves may have an order of magnitude larger error than sine waves under the same conditions. We also show that the effects of data quantity and quality are of critical importance in determining the error in the growth or decay rate, and that the effect of the key parametric variables are modulated by the growth rate itself. We further demonstrate methods by which ensemble and orthogonal data may be introduced to improve the noise response. With regard for the important variables, precise measurement of the growth rates of instabilities may be supplemented with an accurately estimated uncertainty. This opens many new possibilities for the measurement of coherent structure in shear flows. Experiments in Fluids Springer Journals

An error analysis of the dynamic mode decomposition

Loading next page...
Copyright © 2011 by Springer-Verlag
Engineering; Fluid- and Aerodynamics; Engineering Fluid Dynamics; Engineering Thermodynamics, Heat and Mass Transfer
Publisher site
See Article on Publisher Site


You’re reading a free preview. Subscribe to read the entire article.

DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches


Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.



billed annually
Start Free Trial

14-day Free Trial