Integral equation methods are a useful way to look at how sound waves move in structural health monitoring (SHM). These methods naturally work with endless areas, complex borders, and different types of media because they change the form of governing differential equations into integral forms. One important numerical method is the boundary element method (BEM), which lowers the number of dimensions in a problem and speeds up computations. This study looks at different ways to use integral equations, how to use them numerically, and how they can be used to correctly model sound events for finding structure problems in health tracking applications.