Date of Award


Document Type

Thesis - Open Access

Degree Name

Master of Science in Aerospace Engineering


Graduate Studies

Committee Chair

Dr. Dae Won Kim

First Committee Member

Dr. Susan Allen

Second Committee Member

Dr. Sirish Namilae

Third Committee Member

Dr. Andrei Ludu


The objective of this research is to investigate an optimized two-dimensional random pattern of uniformly excited points using the Genetic Algorithm (GA) technique for structural health monitoring. The point excitations generate ultrasonic waves in both isotropic and anisotropic materials that can be effective in diagnosing structural defects. The formed ultrasonic waves can constructively interfere and send out an intense wave beam to a predetermined target. The constructed wave beams can be steered to different directions with variable target distances. In the GA, the cost function is constructed to reduce main lobe beamwidth, eliminate grating lobes and suppress sidelobes’ levels. Mathematical modelling, finite element simulations, and optimizations are successively performed to achieve the objectives.

Secondly Firstly, a mathematical beamforming model is developed to describe the excitation pattern of which each point is excited at the same time delay with a uniform weighting factor. The derived methodology accounts for enclosing all excitations within a certain aperture. The centroid of the emitting sources is also kept at the origin of the Cartesian coordinate within a slight tolerance range. For the near field, in isotropic materials, the excitation points lay on equally spaced circular arcs centered at the target point. In anisotropic materials, such as composites, the wave amplitude and phase velocity are highly dependent on fiber directions. Because of anisotropic nature, the excitation geometry becomes quite complicated.

Secondly, finite element models for aluminum and composite plates are simulated to extract wave characteristics, such as displacement amplitudes, phase velocity profiles and slowness curves. These data are implemented later in the optimization algorithm. A quarter plate of radius 150mm and 1.125mm thickness is modelled as a three-dimensional solid part. A concentrated force with a 2.5 cycle-Hanning window sinusoidal signal is applied at the center of the plate and the boundaries are chosen to be symmetrical. Radial sensors at 5 degrees increments are positioned at 50mm from the excitation source to measure wave properties. The simulation results show that the amplitude and velocity are uniform for isotropic materials whereas the waves propagate rapidly with higher amplitudes along the fibers in anisotropic materials.

Thirdly, after collecting all the required information, a GA optimization technique is applied to generate the excitation population of x- and y-coordinates. The pre-determined population is permutated, cross-overed and mutated so that additional possibilities are produced. The same process is repeated for many generations until the local optimum result is obtained.

Finally, the near field beamforming is plotted in MATLAB at different actuation point numbers for the isotropic and anisotropic materials. The results are then compared to other linear, circular and planar patterns found in literature.