Experiments in Fluids

, 60:31 | Cite as

Automated classification of transient contamination in stationary acoustic data

  • Christopher J. BahrEmail author
  • Todd Schultz
Research Article


An automated procedure for the classification of transient contamination of stationary acoustic data is proposed and analyzed. The procedure requires the assumption that the stationary acoustic data of interest can be modeled as a band-limited, Gaussian random process. It also requires that the transient contamination be of higher variance than the acoustic data of interest. When these assumptions are satisfied, it is a blind separation procedure, aside from the initial input specifying how to subdivide the time series of interest. No a priori threshold criterion is required. Simulation results show that for a sufficient number of blocks, the method performs well, as long as the occasional false positive or false negative is acceptable. The effectiveness of the procedure is demonstrated with an application to experimental wind tunnel acoustic test data which are contaminated by hydrodynamic gusts.

Graphical abstract

List of symbols


Normalized signal bandwidth


Kullback–Leibler divergence


Mach number


Number of samples in a block of data


Sample index


Probability distribution function


Probability density function


Probability distribution function, estimate of P


Probability density function, estimate of p


Individual sample in a block of data


Gamma distribution shape parameter


Gamma distribution scale parameter


Gamma function


Incomplete gamma function


Effective degrees of freedom for signal of block size N

\(\sigma ^2\)

Variance of a block of data

\(\chi ^2_N\)

Sum of the squares of the samples in a block of data



The authors would like to acknowledge the support provided by the 14- by 22-Foot Subsonic Tunnel team, by colleagues in the Aeroacoustics and Advanced Sensing & Optical Measurements branches at the NASA Langley Research Center, and by colleagues in the Aerodynamics, Noise, and Propulsion Laboratory in the Boeing Test & Evaluation organization at The Boeing Company. The hybrid wing body test was funded by the NASA Environmentally Responsible Aviation Project.


  1. Aggarwal CC (2017) Outlier analysis, 2nd edn. Springer, New YorkCrossRefGoogle Scholar
  2. Bahr CJ, Brooks TF, Humphreys WM, Spalt TB, Stead DJ (2014) Acoustic data processing and transient signal analysis for the hybrid wing body 14- by 22-foot subsonic wind tunnel test. In: 20th AIAA, CEAS aeroacoustics conference, AIAA Aviation, Atlanta, GA. AIAA 2014, pp 2014–2345Google Scholar
  3. Bahr CJ, Horne WC (2017) Subspace-based background subtraction applied to aeroacoustic wind tunnel testing. Int J Aeroacoust 16(4–5):299–325CrossRefGoogle Scholar
  4. Bendat JS, Piersol AG (2000) Random data analysis and measurement procedures. Wiley, New YorkzbMATHGoogle Scholar
  5. Cardoso J (1997) Infomax and maximum likelihood for blind source separation. IEEE Signal Process Lett 4(4):112–114CrossRefGoogle Scholar
  6. Coleman HW, Steele WG (1999) Experimentation and uncertainty analysis for engineers, 2nd edn. Wiley, New YorkGoogle Scholar
  7. Hawkins D (1980) Identification of outliers. Springer, New YorkCrossRefGoogle Scholar
  8. Heath SL, Brooks TF, Hutcheson FV, Doty MJ, Bahr CJ, Hoad D, Becker LE, Humphreys WM, Burley CL, Stead DJ, Pope DS, Spalt TB, Kuchta DH, Plassman GE, Moen JA (2016) NASA hybrid wing body aircraft aeroacoustic test documentation report. Tech. Rep. NASA TM-2016-219185Google Scholar
  9. Humphreys WM, Brooks TF, Hunter WW, Meadows KR (1998) Design and use of microphone directional arrays for aeroacoustic measurements. In: 36th AIAA aerospace sciences meeting & exhibit, Reno, NV, AIAA-98-0471Google Scholar
  10. NIST (2013) NIST/SEMATECH e-handbook of statistical methods, chap Gamma Distribution.
  11. Soderman PT, Allen CS (2002) Microphone measurements in and out of airstream, chap 1. In: Mueller TJ (ed) Aeroacoustic measurements. Springer, Berlin, pp 22–24Google Scholar
  12. Ting KM (2010) Confusion matrix. In: Sammut C, Webb GI (eds) Encyclopedia of machine learning. Springer, Boston, p 209Google Scholar
  13. Zelen M, Severo NC (1972) Probability functions, chap 26. In: Abramowitz M, Stegun IA (eds) Handbook of mathematical functions. Dover Publications Inc, New York, pp 940–943Google Scholar
  14. Zhang J (2013) Reducing bias of the maximum likelihood estimator of shape parameter for the gamma distribution. Comput Stat 28(4):1715–1724MathSciNetCrossRefGoogle Scholar

Copyright information

© This is a U.S. government work and its text is not subject to copyright protection in the United States; however, its text may be subject to foreign copyright protection 2019

Authors and Affiliations

  1. 1.Aeroacoustics Branch, NASA Langley Research CenterHamptonUSA
  2. 2.Boeing Test and EvaluationThe Boeing CompanySeattleUSA

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