Proposal for an angle/time-cyclostationary parametric model with application on internal combustion engine analysis - Jambersi, Andreyson Bicudo (2020)
The identification and model-based vibration analysis of a diesel internal combustion engine (ICE) is addressed in this thesis. An angle/time-dependent parametric model is proposed based on the existent well-known functional series time-varying autoregressive moving-average (FS-TARMA) formulation. However, instead of imposes the model coefficients' temporal evolution, this thesis suggests a model in which the coefficients are expanded and modeled as evolving according to an angular-periodic (related to the crankshaft position) basis. Due to this angle/time-dependency, we refer to this new model as an angle/time-FS-ARMA (or AT-FS-ARMA) model. The angular-periodic basis is derived from the AT-cyclostationary framework, a novel class of model extending the only time- or angle-cyclostationary framework. The proposed model considers the angle-periodicities (kinematic-related) often present in vibration-based signals from rotating and reciprocating machines, yet preserving the carrier (time-dependent dynamic). A ``Relaxed'' Multi-Stage Weighted-Least-Squares estimator is used to compute the models. The model structure is selected by evaluating the Bayesian information criterion through the assessment of several candidate models. A comparison between a model-based angle-frequency map and its non-parametric counterpart (obtained through smoothed-pseudo-Wigner-Ville distribution) was performed to show our proposal's potentiality. The results showed that the AT-FS-ARMA-based angle/frequency map provides a useful complementary tool for analysis; it is free from cross-terms and allows one to relate kinematics phenomena to the angular-instants in which they occur.