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This book gives a comprehensive introduction to the Helmholtz Equation Least Squares (HELS) method and its use in diagnosing noise and vibration problems. In contrast to the traditional NAH technologies, the HELS method does not seek an exact solution to the acoustic field produced by an arbitrarily shaped structure. Rather, it attempts to obtain the best approximation of an acoustic field through the expansion of certain basis functions. Therefore, it significantly simplifies the complexities of the reconstruction process, yet still enables one to acquire an understanding of the root causes of different noise and vibration problems that involve arbitrarily shaped surfaces in non-free space using far fewer measurement points than either Fourier acoustics or BEM based NAH. The examples given in this book illustrate that the HELS method may potentially become a practical and versatile tool for engineers to tackle a variety of complex noise and vibration issues in engineering applications.

Engineering. --- Engineering Acoustics. --- Acoustics. --- Vibration, Dynamical Systems, Control. --- Mathematical Modeling and Industrial Mathematics. --- Vibration. --- Acoustics in engineering. --- Ingénierie --- Acoustique --- Vibration --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Civil Engineering --- Sound-waves. --- Sound --- Radiation sources. --- Least squares. --- Helmholtz equation --- Transmission. --- Numerical solutions. --- Method of least squares --- Squares, Least --- Sources of radiation --- Transmission of sound --- Mathematical models. --- Dynamical systems. --- Dynamics. --- Acoustical engineering. --- Numerical analysis --- Curve fitting --- Geodesy --- Mathematical statistics --- Mathematics --- Probabilities --- Triangulation --- Quantum optics --- Radiation --- Architectural acoustics --- Sound-waves --- Soundproofing --- Waves --- Cycles --- Mechanics --- Acoustic engineering --- Sonic engineering --- Sonics --- Sound engineering --- Engineering --- Models, Mathematical --- Simulation methods --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Physics --- Statics --- Industrial applications