This study focusses on probabilistic modelling of the bladed disc system and numerical estimation of the distributions of the response quantities of the system. Stochastic finite element model of the system consisting of all the assemblies and the hub is developed and reported. The spatial inhomogeneity of mistuned structures is modelled as non-Gaussian random field. Experimentally, the system parameters can be measured at the specified locations of the bladed disk structure. In this analysis, a synthetic data is generated which represent this measured data set. Further, Nataf transformation is implemented to each component of the data set to get the polynomial chaos expansion framework of the system parameters. Since, the random field of the system parameter is approximated as correlated random variables, Spearman’s rank correlation coefficient is used in this manuscript to obtain that correlation among the random parameters across the domain. The approximated probability density function obtained through the aforementioned methodology is compared with the target probability density function of the parameter using Kullback–Liebler (KL) entropy as a metric. Also, the same KL entropy is used as a metric to check the convergence of polynomial chaos terms in the expansion. Next, the proposed polynomial chaos method is integrated with commercial finite element software to quantify the propagation of randomness associated with system parameters into the response quantities. Subsequently, the statistical processing helps in estimating the probabilistic measure of the required response quantities. The results obtained through the conventional Monte Carlo (MC) simulations have been used as the benchmark to compare the response characteristics obtained through the proposed algorithm.

This paper presents a procedure for determination of dynamic properties of rolling element bearing by using the vibration signals picked up at the bearing caps. The rotor-bearing assembly is idealized as Duffing oscillator and random vibration signals modelled as exponentially correlated (Ornstein-Uhlenbeck) colored noise. Expressing the excitation as a first order filtered white noise enables the direct formulation of the 3D-Fokker Planck (FP) equation for system response through the Markov vector approach. Closed form solution of the stationary FP equation is derived. Subsequently the response statistics of experimentally obtained random vibration signal are processed through the closed form solution of the FP equation as the inverse process of parameters estimation from the measured response. Further, the dynamic behavior of rigid rotor-bearing system is investigated under combined excitation of white noise and harmonic forces arising due to rotor unbalance force. The effect of system nonlinearities, stiffness, damping and unbalanced excitation force on the dynamic response are investigated using the bifurcation plot. For assessment of structural degradation of bearings, a novel entropy based approach is developed. Experimental studies on roller bearing are carried out to demonstrate the effectiveness of the proposed approach.

Bladed disc systems, are designed to be rotationally periodic i.e. each sector repeats itself in an angular manner. This ensures that the response characteristics preserve this rotational periodicity and is defined as a tuned system. However, due to manufacturing limitations, there are invariably random spatial variations in the sectors which constitute the rotor. This in turn destroys the periodicity (angular symmetry) of the rotor. Such a system is defined as a mistuned system, leads to energy localization and makes the rotor susceptible to damage leading to a loss of its service life. This study focusses on developing a methodology for modeling the random spatial inhomogeneities and integrating with finite element analysis for estimating the behavior of a sector of a rotor blade assembly. Approximations for the non-Gaussian random fields for the spatial inhomogeneities are directly developed from the data set of measurements available from coordinate measuring machine (CMM). Subsequently, Rosenblatt’s transformations are applied to each component of the discrete measurement data set for polynomial chaos (PC) representation of the parameter to get the estimated probability density function (pdf). Spearman’s rank correlation coefficient (SRCC) is calculated to obtain the correlation parameter. Kullback–Liebler entropy (KLE) is used as a metric to compare the estimated pdf obtained through the PC representation of the measured data. The in-house PC based developed codes are subsequently integrated with commercially available finite element software which enable quantifying the propagation of the spatial random uncertainties into the response characteristics. Statistical processing of the response quantities is carried out to estimate probabilistic measures of the corresponding response quantities.

Crossing intensity constitute an important response characteristic for randomly vibrating structures, especially if one is interested in estimating the risk against failures. This paper focusses on developing approximations by which estimates of the crossing intensities for response of marine structures can be obtained in a computationally efficient manner, when the loads are modeled as a special class of non-Gaussian processes, namely as LMA processes. Ocean waves exhibit considerable non-Gaussianity as marked by their skewed marginal distributions and heavy tails. Here, a new class of processes-the Laplace driven Moving Average (LMA) processes are used to model the ocean waves. LMA processes are non-Gaussian, strictly stationary, can model in principle any spectrum and have the additional flexibility to model the skewness and the kurtosis of the marginal distribution. The structure behavior assumed is limited to quadratic systems characterized by second order kernels, which is common for marine structures. Thus, an estimation of the crossing intensities of the response involves studying the crossing characteristics of a LMA process passing through a second order filter. A new computationally efficient hybrid method, which uses the saddle point approximations along with limited Monte Carlo simulations, is developed to compute crossing intensity of the response. The proposed method is illustrated through numerical examples.