We present a statistical analysis of the gravoturbulent velocity fluctuations in molecular cloud complexes extracted from our Cloud Factory galactic-scale ISM simulation suite. For this purpose, we produce non-LTE $^{12}$CO J=1-0 synthetic observations and apply the Principal Component Analysis (PCA) reduction technique on a representative sample of cloud complexes. The velocity fluctuations are self-consistently generated by different physical mechanisms at play in our simulations, which include galactic-scale forces, gas self-gravity, and supernova feedback. The statistical analysis suggests that, even though purely gravitational effects are necessary to reproduce standard observational laws, they are not sufficient in most cases. We show that the extra injection of energy from supernova explosions plays a key role in establishing the global turbulent field and the local dynamics and morphology of molecular clouds. Additionally, we characterise structure function scaling parameters as a result of cloud environmental conditions: some of the complexes are immersed in diffuse (inter-arm) or dense (spiral-arm) environments, and others are influenced by embedded or external supernovae. In quiescent regions, we obtain time-evolving trajectories of scaling parameters driven by gravitational collapse and supersonic turbulent flows. Our findings suggests that a PCA-based statistical study is a robust method to diagnose the physical mechanisms that drive the gravoturbulent properties of molecular clouds. Also, we present a new open source module, the PCAFACTORY, which smartly performs PCA to extract velocity structure functions from simulated or real data of the ISM in a user-friendly way. Software DOI: 10.5281/zenodo.3822718
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