Data-Driven Multiscale Model Identification

In the modern industry, the design and manufacturing processes demand high product quality and lower production costs and times. Moreover, they require the combination of a variety of processes in different levels. These characteristics render them as complex systems. Therefore, the accurate understanding and representation of these systems behavior and dynamics are essential for the development of new techniques aiming at improving the product quality and minimize the costs.

The precise mathematical description of these systems is of main challenge. The combination of system identification and model reduction techniques that provide full insight on the system behavior using the minimum possible amount of data has gained much attention in recent years. The data driven modelling techniques offer flexibility and better accuracy when it comes to system identification. Thus, they render as attractive tools for system identification purposes.

These methods though, are prone to fail when it comes to models with abrupt changes and structures that are mixing high and low frequency effects, the so called multi-scale models. This thesis addresses the existing data-driven algorithms by presenting various examples, justifying the necessity of the development of more efficient algorithms into this direction.

The first part of this thesis analyses the existing reduced order algorithms for data-driven models for temporal and spatio-temporal datasets. The dominant methods and their variations are presented and compared for specific examples that comprise multi-scale characteristics. Reduced order models, such as Subspace identification method (SID) for one-dimensional data, Principal Component Analysis (PCA), Dynamic Mode Decomposition (DMD) and their extensions for both one and two-dimensional data will be addressed. The estimated dynamic systems are analysed and their performance is compared against the original datasets in each example respectively. Their inaccuracies and incapability of fully obtaining the system behavior will be the foundation for the development of identification methods that are more accurate and capable of revealing all system characteristics.

The second part of this thesis proposes a novel multi-scale reduced order POD and DMD method that gives full insight on complex system characteristics. These approaches take advantage of the wavelet decomposition method and divide the given datasets into different levels of resolution before applying the POD or DMD algorithm. By using the proposed algorithm, a novel system identification algorithm is formulated. Complex models with mixed frequency effects and abrupt changes can be estimated accurately. Due the wavelet decomposition properties, they are able to address complex structures into different levels of resolution. Therefore, they can reveal dynamics and model behaviors that cannot be represented from a single scale model
efficiently but neither from the existing multi-resolution algorithms.