Tensor-Train decomposition for image classification problems

In these last years a great effort has been put in the development of new techniques for automatic object classification, also due to the consequences in many applications such as medical imaging or driverless cars. To this end, several mathematical models have been developed from logistic regression to neural networks. A crucial aspect of these so called classification algorithms is the use of algebraic tools to represent and approximate the input data. In this thesis, we examine two different models for image classification based on a particular tensor decomposition named Tensor-Train (TT) decomposition. The use of tensor approaches preserves the multidimensional structure of the data and the neighboring relations among pixels. Furthermore the Tensor-Train, differently from other tensor decompositions, does not suffer from the curse of dimensionality making it an extremely powerful strategy when dealing with high-dimensional data. It also allows data compression when combined with truncation strategies that reduce memory requirements without spoiling classification performance. The first model we propose is based on a direct decomposition of the database by means of the TT decomposition to find basis vectors used to classify a new object. The second model is a tensor dictionary learning model, based on the TT decomposition where the terms of the decomposition are estimated using a proximal alternating linearized minimization algorithm with a spectral stepsize.

Vibro-acoustic analysis and design optimization to improve comfort and sustainability of future passenger aircraft

Due to the interest of general public and the industrial stakeholders, new challenges and demands are rising in aircraft design. The sustainability is taking its place amongst more traditional design factors, such as safety, performances and costs. Sustainability is both environmental and economic, and among the factors contributing to economic sustainability, there is also passengers' comfort. In order to win these two challenges, they must be considered in the early stages of aircraft design. In this work, the focus is on emissions generation and acoustic comfort, aiming at reducing pollution and internal noise in the preliminary design phases. These results can be achieved with both unconventional aircraft configurations and advanced materials, which also require new numerical formulations to be assessed. In this research, on one hand, the windowless configuration for a commercial aircraft is studied with traditional preliminary design methods in order to achieve a weight reduction and consequently a return in terms of emissions and costs. On the other hand, a new class of insulating materials, the acoustic metamaterials, is applied on the passenger cabin lining panels. The complex kinematic behaviour of these advanced materials is studied through the Carrera's Unified Formulation, that enhances a wide class of powerful refined shell and beam theories with a unique formulation.