Reduced order modelling through system identification using stochastic filtering
thesisposted on 2019-06-12, 16:07 authored by Karol Bogdanski
This thesis presents a novel approach to model order reduction, through system identification and using stochastic filtering. Order reduction is a particularly relevant application in the automotive context, as the generation of simplified simulation models for the whole vehicle and its subsystems is an increasingly important aspect of vehicle design.
First, grey-box parameter identification of vehicle handling dynamics is explored, including identification of a combined-slip tyre model. This introductory study serves as an intermediate step to review three alternative stochastic filters: identifying forms of the unscented Kalman filter, extended Kalman filter and particle filter are here compared for effectiveness, complexity and computational efficiency. Despite being initially merely considered as a stepping stone towards black-box identification, this phase of the PhD generated its own and independent outcomes and might be viewed as a spin-off of the main research topic. All three filters appear suited to system identification and could operate in on-line model predictive controllers or estimators, with varying levels of practicability at different sampling rates.
Work on black-box system identification then starts through a non-linear Kalman filter, extended to identify all the parameters of a canonical linear state-space structure. In spite of all model parameters being unknown at the start, the filter is able to evolve parameter estimates to achieve 100$\%$ accuracy in noise-free test cases, and is also proven to be robust to noise in the measurements. The canonical form ensures that a minimal number of parameters need to be identified and produces additional information in terms of eigenvalues and dominant modes.
After extensive testing in the linear domain, state-space is extended into a non-linear framework, with each parameter becoming a non-linear function of system inputs or states. Parameter variation is first constrained by cubic spline polynomials, to provide continuity and maintain relatively small extended state-parameter vectors. This early approach is later simplified, with each element of state-space generated through unconstrained, generic non-linear functions and defined through a number of equally spaced, fixed nodes. Conditioning and convergence are maintained through the definition of additional system outputs, based on specific functions of the non-linear node ordinates. Unlike other methods published in the literature, this new approach does not focus on a specific non-linear structure, but consists in the prescription of a generic and yet simple non-linear state-space model structure, that allows various non-linearities to be identified and approximated solely based on inputs and outputs.
The method is illustrated in practice through simple non-linear examples and test cases, which include the identification of a full vehicle model, a highly non-linear brake model and CFD data. These applications show that it is possible to easily expand the order of the system and the complexity of the non-linearities, to achieve higher accuracy while ensuring good parameter conditioning. The approach is completely black-box and requires no physical understanding of the process for successful identification, making it an ideally suited mechanism for order reduction of high order simulation models. In addition to high order simulation data, the developed approach can be used as a tool for conventional system identification and applied to experimental test data as well.