Wind turbine power curve modeling is an important tool in turbine performance monitoring and power forecasting. There are several statistical techniques to fit the empirical power curve of a wind turbine, which can be classified into parametric and nonparametric methods. In this paper, we study four of these methods to estimate the wind turbine power curve. Polynomial regression is studied as the benchmark parametric model, and issues associated with this technique are discussed. We then introduce the locally weighted polynomial regression method, and show its advantages over the polynomial regression. Also, the spline regression method is examined to achieve more flexibility for fitting the power curve. Finally, we develop a penalized spline regression model to address the issues of choosing the number and location of knots in the spline regression. The performance of the presented methods is evaluated using two simulated data sets as well as an actual operational power data of a wind farm in North America.Index Terms-Nonparametric regression, penalized spline regression, polynomial regression, wind energy, wind turbine power curve.

Background: Detection of vertebral fractures (VFs) aids in management of osteoporosis and targeting of fracture prevention therapies.Purpose: To determine whether convolutional neural networks (CNNs) can be trained to identify VFs at VF assessment (VFA) performed with dual-energy x-ray absorptiometry and if VFs identified by CNNs confer a similar prognosis compared with the expert reader reference standard. Materials and Methods: In this retrospective study, 12 742 routine clinical VFA images obtained from February 2010 to December 2017 and reported as VF present or absent were used for CNN training and testing. All reporting physicians were diagnostic imaging specialists with at least 10 years of experience. Randomly selected training and validation sets were used to produce a CNN ensemble that calculates VF probability. A test set (30%; 3822 images) was used to assess CNN agreement with the human expert reader reference standard and CNN prediction of incident non-VFs. Statistical analyses included area under the receiver operating characteristic curve, two-tailed Student t tests, prevalence-and bias-adjusted k value, Kaplan-Meier curves, and Cox proportional hazard models.Results: This study included 12 742 patients (mean age, 76 years 6 7; 12 013 women). The CNN ensemble demonstrated an area under the receiver operating characteristic curve of 0.94 (95% confidence interval [CI]: 0.93, 0.95) for VF detection that corresponded to sensitivity of 87.4% (534 of 611), specificity of 88.4% (2838 of 3211), and prevalence-and bias-adjusted k value of 0.77. On the basis of incident fracture data available for 2813 patients (mean follow up, 3.7 years), hazard ratios adjusted for baseline fracture probability were 1.7 (95% CI: 1.3, 2.2) for CNN versus 1.8 (95% CI: 1.3, 2.3) for expert reader-detected VFs for incident non-VF and 2.3 (95% CI: 1.5, 3.5) versus 2.4 (95% CI: 1.5, 3.7) for incident hip fracture. Conclusion:Convolutional neural networks can identify vertebral fractures on vertebral fracture assessment images with high accuracy, and these convolutional neural network-identified vertebral fractures predict clinical fracture outcomes.

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