## 7 Discussion  
In this study, four data sets comprising strains measured on the NDP model riser subjected to uniform and sheared currents were employed to test empirical fatigue damage estimation methods. Five empirical methods were studied--they include Weighted Waveform Analysis (WWA), modified WWA, Proper Orthogonal Decomposition (POD), Modal Phase Decomposition (MPR), and a hybrid method that combines MPR and modified WWA. For each method, the theoretical formulation was first presented briefly and then its application was illustrated by an example wherein a single sensor was selected as the target sensor and by using measurements from the remaining twenty-three sensors as inputs, the riser response was reconstructed at the location of the target sensor. The fatigue damage estimated using the reconstructed riser response was compared with the value based directly on measurements at that target. The ratio between the estimated fatigue damage and that based on measurements there was used as an indicator of the accuracy of the empirical method. Two separate summary studies--one involving a larger number of available sensors on the riser (twenty-three) and another involving a small number (eight)--were carried out and the estimated fatigue damage over the entire length of the NDP model riser was calculated and the results discussed. Based on the numerical studies presented, some concluding remarks follow:  
1. With careful selection of the riser modes for inclusion, the WWA method has the ability to preserve higher harmonics in the reconstructed riser response since the selected modes in the method are non-sequential. Because the modal weights are solved for at each time instant, non-stationary characteristics, if present, have a limited influence on response reconstruction with this method. The WWA method works particularly well if only a small number of sensors is available and it relies on assumed mode shapes that are based on knowledge of the physical properties of the riser. Computation with the WWA method is fast. 2. The modified WWA method can account for the influence of higher harmonics as long as a large number of sensors is available. This method is more versatile than the WWA method in accounting for the effect of traveling waves. Like the WWA method, it also accounts for non-stationary characteristics, but it is not well-suited for cases where only a small number of sensors is available since a greater number of modal weights need to be estimated than with WWA. The modified WWA method relies on assumed mode shapes and computation is fast. 3. The POD method preserves frequency components and higher harmonics in the reconstructed riser response by empirical decomposition of the spatio-temporal data. This is evident from the power spectra as well as curvature plots that reveal high-frequency energy and large curvatures (or small wavelengths). POD only relies entirely on the data collected; the method identifies empirical mode shapes directly from the data, without the need for knowledge of the physical properties of the riser. The POD scheme is the fastest among the five methods; however, POD does not account for non-stationary response characteristics. The method is not well-suited when only a small number of sensors is available because of inaccuracies in the reconstructed response that arise due to the need for spatial interpolation or extrapolation from discrete empirical modes to any target location. 4. As is the case for the POD method, the MPR method accounts for higher harmonics in the response and only relies on data, not on physical properties of the riser to estimate complex riser modes. MPR, however, is not well-suited to situations where the riser response exhibits strong non-stationary characteristics or when only a small number of sensors is available. Computationwith the MPR method is slow. Importantly, MPR explicitly accounts for traveling waves in decomposing the measured response.