Gravitational waves are weak propagations of spacetime energy containing crucial astrophysical information on some of the most energetic events in the universe, such as black hole mergers and supernovae. In this study, Bayesian modelling is used for estimating complex sinusoidal waveforms from supernovae, utilising variants of Markov Chain Monte Carlo (MCMC) simulations to estimate these waveforms. Principal Component Analysis (PCA) combined with regression, and artificial intelligence techniques, specifically the use of causal structure discovery algorithms, are used to identify the correct selection of PC components for intelligent analysis. To facilitate causal structure discovery, an alternative expression of individual waveform structure must be determined, and Waveform Population Gradients (WPGs) was specifically developed to represent each possible waveform structure. An artificial intelligence model known as a Bayesian network is developed to perform classification of waveform structures and probabilistic inference of complex supernovae models. These developments are useful for advancing intelligent analysis in gravitational wave studies, astrophysics and beyond.