On spectral representation method and Karhunen-Loeve expansion in modelling construction material properties

Randomness in construction material properties (e.g. Young's modulus) can be simulated by stationary random processes or random fields. To check the stationarity of commonly used techniques, three random process generation methods were considered: X-n(t), Y-n(t), and Z(n)(t). Methods X-n(t) and Y-n(t) are based on a truncation of the spectral representation method with the first n terms. X-n(t) has random amplitudes while Y-n(t) has random harmonics phases. Method Z(n)(t) is based on the Karhunen-Loeve expansion with the first n terms as well. The effects of the truncation technique on the mean-square error, covariance function, and scale of fluctuation were examined in this study; these three methods were shown to have biased estimations of variance with finite n. Modified forms for those methods were proposed to ensure the truncated processes were still zero-mean, unit-variance, and had a controllable scale of fluctuation; in particular, the modified form of Karhunen-Loeve expansion was shown to be stationary in variance. As a result, the modified forms for those three methods are advantageous in simulating statistically homogenous material properties. The effectiveness of the modified forms was demonstrated by a numerical example. (C) 2017 Politechnika Wroclawska. Published by Elsevier Sp. z o.o. All rights reserved.