Institute of Fundamental Technological Research

In this paper, the basic methodology for the fatigue reliability assessment of randomly vibrating multidegree-of-freedom systems is presented within the coupled response-degradation model. The fatigue process in the system components is quantified by the fatigue crack growth equations which—via the stress range—are coupled with the system response. Simultaneously, the system dynamics is affected by fatigue process via its stiffness degradation so that it provides the actual stress values to the fatigue growth equation. In addition to the general coupled response-degradation analysis, its special case of noncoupled fatigue crack growth is treated as well for the wide-band stationary applied stress by the use of its first four spectral moments and the approximate, empirically motivated, Dirlik’s probability distribution for the stress range. Both, the general analysis and the illustrating exemplary problems elaborated in the paper provide the route to the fatigue reliability estimation in complex–hierarchical vibratory systems under random loading.

Fatigue, Crack growth, Random vibration, System reliability, Stiffness degradation

This paper provides a methodology for optimal prediction of the response of randomly vibrating structures using information from a limited number of measurements. The objective is to optimize the locations of sensors for the purpose of making the most accurate predictions of the response at unmeasured locations in structural systems. The kriging method is used to find the response predictions and the corresponding mean-square errors at unmeasured locations. The mean-square errors in the predictions depend on the locations of sensors and the correlation characteristics of the response evaluated from the model of dynamics and the characteristics of the excitation. The response predictions depend also on the information contained in measurements. The optimal sensor locations are selected to minimize the total mean-square error of the response predictions at unmeasured points. This leads to a complicated non-convex optimization problem in which multiple local and global optima may exist. A hybrid optimization method based on evolution strategies is used to determine a global minimum. The optimal experimental design method presented in the paper is illustrated by designing the optimal sensor locations for an elastic beam and a plate subjected to a class of random stationary loads.

Structures, Random vibrations, Sensor locations, Kriging, Evolution strategies