#### Date of Award

8-2016

#### Degree Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Mechanical Engineering

#### First Advisor

John S. Bolton

#### Second Advisor

Patricia Davies

#### Committee Chair

John S. Bolton

#### Committee Co-Chair

Patricia Davies

#### Committee Member 1

Mark R. Bell

#### Committee Member 2

Kai M. Li

#### Abstract

Motivated by the need to develop efficient acoustics simulations for sources in different room environments, a modeling procedure has been proposed that consists of two steps in general: (1) the modeling of the free-space radiation of the source based on measurements in a anechoic environment, and (2) the prediction of the sound field in a room environment based on that free-space information.

To achieve a high modeling efficiency, i.e., to reduce the number of modeling parameters while still maintaining acceptable accuracy, a Multipole Equivalent Source Model (ESM) with undetermined source locations has been developed for the free-space sound field prediction. In contrast with traditional ESM’s, or acoustical holography methods in general, the model developed in the present work possesses two efficiency improvements: (1) the use of the series of monopoles, dipoles, quadrupoles, etc. as equivalents sources (since in predicting the sound field, the multipole series can be simply represented as closely located monopoles) and (2) the flexibility of using spatially separated sources with undetermined locations. In the inverse parameter estimation process of this method, the calculation of the source strengths is linear while the source locations are determined by a nonlinear optimization procedure. It is shown, by an experimental validation, that the prediction using this method can be accurate for almost the whole audio frequency range.

To model the sound field at high frequencies specifically, different types of methods using local-basis functions were developed. At high frequencies, the spatial variation of the sound field is usually large and thus the number of measurements points in space is likely not to be enough to model a relatively complicated source if a traditional equivalent source model is used, and the under-sampling errors from all regions will accumulate to affect the predictions in any particular region. However, if localized basis functions are used to represent the sound field, the under-sampling errors from different regions do not affect each other. Two types of local-basis method are developed in this work: one based on piece-wise polynomial interpolation (which is limited to having only a single source) and the other based on least squares (which can be applied to multiple sources and even to interior problems). Simulation results have shown that these local-basis methods, at very high frequencies, can achieve good overall prediction accuracy with only a loss of some details in the spatial variation of the sound field.

In the room acoustics modeling section, the Equivalent Source Method is modified and implemented which, compared with the geometric acoustics models, gives a prediction based on a more rigorous mathematical foundation and, compared with Boundary Element methods, reduces the computational intensity. In this proposed room acoustics ESM, the free-space source radiation is assumed known, and the room component sound field is determined by an ESM. Differing from the free-space ESMs, this room acoustics ESM (1) contains additional equivalent sources representing the incoming waves, and (2) uses impedance boundary conditions on the surfaces instead of the measured sound field, to estimate the source strengths. It is validated by simulations (in both 2D and 3D spaces) and then by experiments that the proposed room acoustics ESM can be used as a reduced order modeling technique in simulating the sound field in a room. It is also shown that the prediction accuracy and the computational load can be flexibly balanced, if Multipole ESMs are used, by selecting an appropriate maximum source order.

#### Recommended Citation

Liu, Yangfan, "Efficient modeling of sound source radiation in free-space and room environments" (2016). *Open Access Dissertations*. 801.

https://docs.lib.purdue.edu/open_access_dissertations/801