Correlation regimes in fluctuations of fatigue crack growth

This paper investigates correlation properties of fluctuations in fatigue crack growth of polycrystalline materials, such as ductile alloys, that are commonly encountered in structures and machinery components of complex electromechanical systems. The model of crack damage measure indicates that the fluctuations of fatigue crack growth are characterized by strong correlation patterns within short time scales and are uncorrelated for larger time scales. The two correlation regimes suggest that the 7075-T6 aluminum alloy, analyzed in this paper, is characterized by a micro-structure which is responsible for an intermittent correlated dynamics of fatigue crack growth within a certain scale. The constitutive equations of the damage measure are built upon the physics of fracture mechanics and are substantiated by Karhunen-Lo\`{e}ve decomposition of fatigue test data. Statistical orthogonality of the estimated damage measure and the resulting estimation error is demonstrated in a Hilbert space setting.Comment: 30 pages, 8 figures, to appear in Physica

Towards Efficient Maximum Likelihood Estimation of LPV-SS Models

How to efficiently identify multiple-input multiple-output (MIMO) linear parameter-varying (LPV) discrete-time state-space (SS) models with affine dependence on the scheduling variable still remains an open question, as identification methods proposed in the literature suffer heavily from the curse of dimensionality and/or depend on over-restrictive approximations of the measured signal behaviors. However, obtaining an SS model of the targeted system is crucial for many LPV control synthesis methods, as these synthesis tools are almost exclusively formulated for the aforementioned representation of the system dynamics. Therefore, in this paper, we tackle the problem by combining state-of-the-art LPV input-output (IO) identification methods with an LPV-IO to LPV-SS realization scheme and a maximum likelihood refinement step. The resulting modular LPV-SS identification approach achieves statical efficiency with a relatively low computational load. The method contains the following three steps: 1) estimation of the Markov coefficient sequence of the underlying system using correlation analysis or Bayesian impulse response estimation, then 2) LPV-SS realization of the estimated coefficients by using a basis reduced Ho-Kalman method, and 3) refinement of the LPV-SS model estimate from a maximum-likelihood point of view by a gradient-based or an expectation-maximization optimization methodology. The effectiveness of the full identification scheme is demonstrated by a Monte Carlo study where our proposed method is compared to existing schemes for identifying a MIMO LPV system