A newly developed real time operating data expansion technique [1-5] has been successfully used for the identification of more detailed information from limited sets of data. This expansion has mainly been used to augment the limited data acquired and allows for better overall visualization of these transient types of events. This technique has mainly been used for general response characteristics for structures. In this work, these expansion techniques are further developed and extended in conjunction with the finite element mass and stiffness matrices to provide information at all of the finite element DOFs from these limited sets of measured data points. This allows for the identification of the dynamic stress and the dynamic strain to be identified from measured transient events, thereby enabling the estimation of fatigue accumulation or usage. One way to predict the transient response and the associated dynamic stresses in the structure is to use the finite element analysis. An accurate model renders the finite element method of analyzing the dynamic stresses and strains extremely useful. But one of the challenges with the finite element analysis is correctly depicting the boundary conditions that the structure will undergo during operation. Also there is no accurate way to exactly represent the transient loads (for example, the wind loads) on the structure. Statistical and probabilistic approaches have to be used to estimate the forces that the structure undergoes during such transient events, but does not provide information due to specific events. Finite element models have been used over the years to estimate the stresses induced in a component due to dynamic loads. Most of the work published in this area has been application oriented. Among such works, one which deals with the issue of dynamic stresses from a broader perspective using a modal analysis technique is presented in [6]. The failure of a mechanical component is examined by performing modal analysis using the finite element approach and then evaluating stresses in the component using a boundary element approach in [6]. Super-element method and global-local approach have also been used in the finite element modeling domain to enhance the accuracy of the models [7]. A finite element model is used as the base model to generate transient response of a vehicle body structure and then using the Modal Stress Method (for estimating global stress distribution) and the Component Mode Synthesis (for local stress time history), the fatigue life of the structure is estimated by Huang et al., [8]. Dynamic stresses in a structure have also been obtained from measured acceleration data using the normal mode analysis in [9]. In such a case, only a limited number of sensors provide the stress information, and are not always able to show critical stress concentration or accumulation. From their inception in the early 80’s, wind turbines have experienced fatigue problems. Virtually all the turbines built in California have experienced fatigue problems in sites with an average wind speed of 7 m/s or more. Blades have been repaired or replaced on most of the turbines. This led the wind energy community to study the fatigue life and probability of failure extensively [10, 11]. Several approaches have been developed [12], [13] and [14] to represent a structure’s fatigue. Typically wind loads are estimated using the parametric or empirical modeling approaches [15]. Parametric models define the response, statistically with respect to the input conditions. Such models fit analytical distribution (Rayleigh or exponential fit) functions to the measured or the simulated data. The parameters of these distribution functions can be useful in defining the response/loads as a function of the input conditions. The end result then is a full statistical definition of the loads over all input conditions. The problem is that the Rayleigh distribution appears to be appropriate only for a single location on a single type of wind turbine (flatwise loads on vertical axis wind turbines). The exponential fit is rather complex in the sense that the starting point of the exponential fit is not very clear. Also as observed in [16], the exponential fit is not always the appropriate choice. The most prevalent alternative to parametric modeling is an empirical distribution of loads (a histogram describing frequency of occurrence of the modeled response quantity). For empirical models, the results of one ten-minute simulation for each wind speed bin are “cycle counted” and the number of cycles are multiplied by 20 year duration to extrapolate the fatigue loads to 20 years. According to [17], this method is flawed in at least two ways. First, it does not account for rare events and second, because the simulations do not capture accurate extreme statistics they do not estimate the peak load which will occur over the operating life of the machine. A modal superposition method is used in [18] to resolve the forced vibration equation for a finite element model so as to use it to calculate the corresponding stress values. Estimating the damping values in the model can create problems in such a technique. Work has been done to evaluate the stress concentration regions and to estimate the stress-strain using different techniques. Dynamic forces and the stresses can be calculated [19] using a static model and a dynamic correction factor based on the modal accelerations at small number of the modal DOFs. Strain measurements taken at certain locations in a structure are used to analytically synthesize the frequency responses at those locations where no data was collected by Powell [20]. Using the stress-strain information, the decision on where to make structural modification is made. Blade element theory [21] is used to calculate the aerodynamic loads for small wind turbine blades. Using the load information 202
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