A Weighted Least Squares Approach for the Design of Adaptive Aerodynamic Structures Subjected to an Out-Of-Plane Transformation

2018 ◽  
Author(s):  
Fuzhao Mou ◽  
Hamid Khakpour Nejadkhaki ◽  
Aaron Estes ◽  
John Hall
Keyword(s):  
Least Squares ◽  
Weighted Least Squares ◽  
Turbine Blades ◽  
Operating Conditions ◽  
Torsional Stiffness ◽  
Power Coefficient ◽  
Mathematical Framework ◽  
Complex Needs ◽  
Least Squares Approach ◽  
The Ideal

An optimal design framework for adaptive wind turbine blades is presented. A mathematical framework establishes the topology of actuators and material compliance. These parameters are selected to adapt the blade twist distribution into a range of prescribed blade configurations. Our previous work established the ideal twist distribution configurations. The distributions improve the aerodynamic efficiency for a range of wind speeds in which the system operates at partial production. Within this range the nonlinear blade twist distribution changes in relation to the speed. The possibility of producing adaptively compliant structures is becoming increasingly possible with innovative materials and additive manufacturing (AM) processes. Our overarching goal is to create a comprehensive design infrastructure that integrates manufacturing and materials innovation with the complex needs of adaptive structures. This work proposes a method through which the ideal twist distribution can be actualized in structural implementation. The implementation involves a modular blade composed of flexible sections whose twist is modulated by actuators along the blade. Each flexible blade section is composed of two contiguous segments, each with a different torsional stiffness defined by a stiffness ratio. The stiffness variation within each section allows the blade to assume a nonlinear twist distribution when actuated. Errors relative to an ideal twist distribution are minimized by optimizing the stiffness ratios and twist actuator locations. The optimization is completed using a weighted least squares approach that allows the blade designer to bias blade performance toward different operating conditions. A quadratic weighting scheme that penalizes twist errors toward the blade tip is found to result in a higher power coefficient than other weighting schemes.

Weighted Least Squares Approach for an Adaptive Aerodynamic Engineered Structure With Twist Transformation

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Fuzhao Mou ◽  
Hamid Khakpour Nejadkhaki ◽  
Aaron Estes ◽  
John F. Hall
Keyword(s):  
Wind Speed ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Twist Angle ◽  
Rayleigh Distribution ◽  
Torsional Stiffness ◽  
Support Design ◽  
Partial Load ◽  
Blade Section ◽  
Least Squares Approach

A design concept for a wind turbine blade with an adaptive twist transformation is presented. The design improves partial-load wind capture by adapting the twist distribution in relation to wind speed. Structural adaptability is enabled by actuating a series of compliant sections that are mounted on a relatively rigid spar. The sections are assumed to have a unique stiffness that is achievable through additive manufacturing technology. The authors' prior work employed an aerodynamic model to establish the theoretical blade twist distribution as a function of wind speed. The work in this paper focuses on a method to optimize the stiffness of each blade section that has been previously defined. A mathematical model is proposed to support design optimization. The model is parameterized in terms of actuator locations and the torsional stiffness ratios of each blade section. These parameters are optimized to allow the blade to adapt its twist distribution to match the prescribed configurations. The optimization is completed using a weighted-least squares approach that minimizes the error between the theoretical and practical design. The selected solution is based upon the configuration that maximizes production. Weights are assigned to bias the performance of the blade toward different operating regimes. Our results indicate that quadratically penalizing twist angle errors toward the blade tip increases power capture. A Rayleigh distribution is used to create three sets of wind data, which vary in average speed. These sets of data are used to evaluate the performance of the proposed blade and design technique.

scholarly journals On the Use of Weighted Least-Squares Approaches for Differential Interferometric SAR Analyses: The Weighted Adaptive Variable-lEngth (WAVE) Technique

Sensors ◽  
2020 ◽  
Vol 20 (4) ◽  
pp. 1103
Author(s):  
Francesco Falabella ◽  
Carmine Serio ◽  
Giovanni Zeni ◽  
Antonio Pepe
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Variable Length ◽  
Mathematical Framework ◽  
Ground Displacement ◽  
Phase Measurements ◽  
Temporal Sampling ◽  
Wave Technique ◽  
Interferometric Sar

This paper concentrates on the study of the Weighted Least-squares (WLS) approaches for the generation of ground displacement time-series through Differential Interferometric SAR (DInSAR) methods. Usually, within the DInSAR framework, the Weighted Least-squares (WLS) techniques have principally been applied for improving the performance of the phase unwrapping operations as well as for better conveying the inversion of sequences of unwrapped interferograms to generate ground displacement maps. In both cases, the identification of low-coherent areas, where the standard deviation of the phase is high, is requested. In this paper, a WLS method that extends the usability of the Multi-Temporal InSAR (MT-InSAR) Small Baseline Subset (SBAS) algorithm in regions with medium-to-low coherence is presented. In particular, the proposed method relies on the adaptive selection and exploitation, pixel-by-pixel, of the medium-to-high coherent interferograms, only, so as to discard the noisy phase measurements. The selected interferometric phase values are then inverted by solving a WLS optimization problem. Noteworthy, the adopted, pixel-dependent selection of the “good” interferograms to be inverted may lead the available SAR data to be grouped into several disjointed subsets, which are then connected, exploiting the Weighted Singular Value Decomposition (WSVD) method. However, in some critical noisy regions, it may also happen that discarding of the incoherent interferograms may lead to rejecting some SAR acquisitions from the generated ground displacement time-series, at the cost of the reduced temporal sampling of the data measurements. Thus, variable-length ground displacement time-series are generated. The mathematical framework of the developed technique, which is named Weighted Adaptive Variable-lEngth (WAVE), is detailed in the manuscript. The presented experiments have been carried out by applying the WAVE technique to a SAR dataset acquired by the COSMO-SkyMed (CSK) sensors over the Basilicata region, Southern Italy. A cross-comparison analysis between the conventional and the WAVE method has also been provided.

Calibration in a closed system: the case of X-ray diffraction analysis

2007 ◽  
Vol 40 (4) ◽  
pp. 694-701
Author(s):  
Thaung Lwin
Keyword(s):  
Diffraction Analysis ◽  
Least Squares ◽  
Functional Relationship ◽  
Weighted Least Squares ◽  
Ordinary Least Squares ◽  
X Ray Diffraction ◽  
Unknown Parameters ◽  
X Ray ◽  
Relationship Model ◽  
Least Squares Approach

Knudsen [X-ray Spectrom.(1981),10, 54–561] proposed and demonstrated a least-squares approach to estimating the unknown parameters of a system of equations required for calibration in X-ray diffraction analysis. The approach is an ordinary least-squares approach which does not incorporate information on the errors of the measured intensities for a set of samples used as standards. The purpose of the present paper is to show that a functional relationship model can be applied to the problem to account for all the variation due to sampling and measurement error in the peak intensities. It is also shown that Knudsen's calibration estimator can be regarded as an approximation to a more general and potentially more efficient weighted least-squares estimator derived from the functional relationship model. The closeness of the approximation depends on the nature of the covariance structure of the intensity measurements.

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