Karhunen–Loève modes obtained from displacement and velocity fields: Assessments and comparisons

The Karhunen–Loève (KL) decomposition method can be used to expand a random process into series of deterministic functions (or KL modes) with uncorrelated random variables as the decomposition coefficients. In vibration analysis, the KL theory is classically developed from the displacement field. In this study, the displacement field, velocity field and displacement–velocity field are used with the KL theory based on an averaging operator involving time and ensemble averages. The three families of KL modes are compared and interpreted in terms of normal modes in the case of linear vibrating systems subjected to white-noise excitation.