This article-based thesis consists of a collection of four journal papers (one accepted, one submitted pending reviews, two in the process of submission), and one conference paper (accepted and presented at InterNoise 2022). Each article relates to a chapter written and formatted in manuscript form. The purpose of this work is to investigate the validity of using Machine Learning to deal with recovering parameters non-intrusively. These parameters range from estimating the amplitudes, wavelengths and phases for direct surface reconstruction for static surface recovery, and the average surface velocity, and water depth for dynamic river free-surfaces. This is done both acoustically on a rough surface, and optically on dynamic rough surfaces. Treating the inverse problem with a machine learning approach allows for further analysis of the problem. For example, getting spatial uncertainty for a given reconstruction, or analysing the behaviour of the trained model as opposed to more traditional approaches. Within this thesis, the Kirchhoff Approximation is used as the underlying acoustic scattering model due to the types of surfaces investigated, the accuracy of the model, and the fast computation time. This model is then used to generate the data required for training. Further to this, the frequency-wavenumber spectrum of dynamic free-surface fluctuations of shallow turbulent flow is exploited.
Firstly, a random forest is trained on data generated from the Kirchhoff approximation in order to recover parameters of a harmonic surface at a given acoustic frequency. It is shown that this generalises well to unseen surfaces, and out-competes methods that utilise the small amplitude assumption. Different metrics are presented to show the applicability of the random forest framework over different source incident angles, and source frequencies.
An acoustic source with a broadband nature was exploited to get some estimation of prediction error. For each frequency, data was generated and models were trained. This allowed for the spread of predicted parameters to be estimated.
In order to recover a wider range of rough surfaces, as well as to get statistical information, a stochastic method named Metropolis-Hastings was introduced to the problem. This competed well with the random forest predictions for the single harmonic, while giving spatial uncertainty. This was extended to a more complicated roughness profile consisting of a summation of many harmonics at different wavelengths. It was found that the profile was recovered well in a region of approximately 33\% of the full profile. In this region, the credible interval decreased substantially. This fact can be used to infer the region of interest, without needing to know the underlying truth of the surface.
Finally, the recovery of the velocity and the depth of shallow-turbulent flows through the application of Metropolis-Hastings and the frequency-wavenumber spectrum to series of images of the flow surface, obtained in laboratory and in-field experiments, was attempted. First, the surface frequency-wavenumber spectrum recovered from a Digital Image Correlator was analysed. This, and data from a CCTV camera over the River Sheaf, was used in the Metropolis-Hastings algorithm. It was found that the velocity was well recovered, and the resulting distributions of the velocity were useful in the extraction of reliable credible intervals. However, the method struggled to recover the depth.
The work presented in this thesis provide an approach to increase the accuracy of recovery from static surface acoustic recovery, while also including a highly informative representation of uncertainty in the spatial domain. Further, this thesis paves the way in new inversion methods using cameras to get information such as the mean surface velocity and can be used to automatically extract the gravity-capillary waves from the captured video leaving a representation that is ready to be exploited.
