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On using polynomial chaos for modeling uncertainty in acoustic propagation
1U.S. Naval Research Laboratory, Washington, DC 20375, USA.
The Journal of the Acoustical Society of America
|April 29, 2006
Summary
Polynomial chaos effectively models environmental variability in acoustic propagation. Low-order polynomial chaos works well for small environmental fluctuation correlation lengths, but higher orders are needed for larger lengths.
Area of Science:
- Acoustics and Wave Propagation
- Computational Physics
- Environmental Modeling
Background:
- Environmental variability significantly impacts acoustic propagation models.
- Stochastic processes are crucial for describing random environmental conditions.
- Accurate wave field representation is essential for reliable propagation predictions.
Purpose of the Study:
- To investigate the application of polynomial chaos for incorporating environmental variability into simplified acoustic propagation models.
- To analyze the accuracy, implementation, and computational aspects of polynomial chaos in wave propagation.
- To determine the influence of environmental fluctuation correlation length on the convergence of polynomial chaos expansions.
Main Methods:
- Utilized a simplified one-dimensional acoustic propagation model.
- Employed a spectral representation for environmental variability as a stochastic process.
- Developed a chaotic representation of the wave field using orthogonal random polynomials.
- Analyzed implementation challenges, approximation accuracy, and computational burden.
Main Results:
- Low-order polynomial chaos expansions are effective when the environmental fluctuation correlation length is small.
- High-order approximants and range-dependent convergence are required for large correlation lengths.
- The findings are applicable to both one-dimensional and higher-dimensional propagation problems.
Conclusions:
- Polynomial chaos is a viable method for modeling environmental variability in acoustic propagation.
- The correlation length of environmental fluctuations critically affects the required order and convergence of polynomial chaos expansions.
- The study provides insights into the practical implementation and limitations of polynomial chaos in wave propagation modeling.
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