Weighted-Least Squares Optimization Method for Control and Shape Design of an Adaptive Blade Twist Distribution to Increase Wind Capture

2018 ◽  
Author(s):  
Fuzhao Mou ◽  
Hamid Khakpour Nejadkhaki ◽  
Aaron Estes ◽  
John Hall
Keyword(s):  
Wind Speed ◽  
Least Squares ◽  
Weighted Least Squares ◽  
Twist Angle ◽  
Torque Control ◽  
Shape Design ◽  
Mathematical Framework ◽  
Relative Stiffness ◽  
Partial Load ◽  
And Control

This paper presents a novel wind turbine blade with an actively adaptable twist angle. A weighted-least square technique is proposed to design and control the blade in its application. Controlling the twist distribution provides new capabilities that may not be achievable with blade pitch or rotor torque control. An adaptive twist angle can reduce fatigue loads and improve the efficiency of wind energy conversion. Our previous work established the theoretical blade twist distribution that maximizes wind capture during partial load operation. The twist distribution changes continuously as a function of wind speed. In practice, it is a challenge to design and control the blade to adapt to this range of transformation. Accordingly, a blade concept and engineering design method are proposed to achieve this task. The blade is constructed from additively manufactured sections that are assumed to have tunable stiffness. The sections are mounted on a centralized spar that provides stiffness. The sections are actuated at each end and have two zones of stiffness. A mathematical framework prescribes (1) length of each blade section and (2) the relative stiffness between a pair of compliant shells. Establishing the section length effectively sets the points of actuation, while the relative stiffness establishes a nonlinear twist. These design selections determine the twist distribution. The method employing weighted-least squares is employed to optimize these selections. The approach biases the shape design and control towards the theoretical twist distribution at a range of designated wind speed. This enables a customized solution that maximizes the wind capture based on the wind conditions at a given installation site.

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.

Variable Twist Blade Transformation to Improve Wind Turbine Performance

2018 ◽  
Author(s):  
Hamid Khakpour Nejadkhaki ◽  
John F. Hall
Keyword(s):  
Wind Speed ◽  
Wind Turbine ◽  
Mechanical Design ◽  
Twist Angle ◽  
Full Range ◽  
Design Procedure ◽  
Angle Distribution ◽  
Design Algorithm ◽  
Aerodynamic Efficiency ◽  
Partial Load

A concept for an innovative wind turbine blade with an actively transformable twist distribution is presented. A simulation model demonstrates that adapting the blade twist distribution can increase the aerodynamic efficiency during partial-load operation. A blade concept consisting of a rigid spar that is surrounded by deformable modular shells is also proposed. The outer shells are assumed to be produced using additive manufacturing (AM) technology. Integrated features enabled by the AM process tune the stiffness, and thus the degree of flexibility for each surrounding segment. The unique local stiffness and the placement of actuators establishes a nonlinear twist angle distribution (TAD). An optimal design procedure is devised for setting the stiffness and actuator locations. It maximizes the aerodynamic efficiency for a discrete range of wind speed. The blade performance is quantified using data acquired from the National Renewable Energy Laboratory (NREL) Aerodyn software. A computer cluster is used to facilitate this process. It must consider the TAD for the range of wind speed that corresponds to the partial-load operation. The design procedure first establishes the TAD geometry based on the theoretical aerodynamic modeling. The TAD geometry is then passed to a mechanical design algorithm. At this point, the actuator positions are set, and the stiffness ratios of the adaptable shells are defined using the objective function. It minimizes the amount of deviation between the actual TAD and that found in the aerodynamic analysis. The free-shape TAD is determined in the final step. This is the shape of the blade when no actuation force is applied to the shells. This shape is then selected to minimize the amount of deflection needed to shape the TAD between its extreme positions. A case study demonstrates the ability of the blade and the proposed design process. The study indicates that a blade with five actuators can achieve the full range of TAD motion. The final solution shows that the adaptive TAD can increase the efficiency by 3.8 and 3.3%, respectively, at the cut-in and rated speeds.

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.

Evaluation for estimating of the PDF and the CDF of Generalized Inverted Exponential Distribution with Application in Industry

2020 ◽  
pp. 507-522
Author(s):  
Parisa Torkaman
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Mean Squared Error ◽  
Weighted Least Squares ◽  
Real Data ◽  
Minimum Variance ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Data Set ◽  
Better Than

The generalized inverted exponential distribution is introduced as a lifetime model with good statistical properties. This paper, the estimation of the probability density function and the cumulative distribution function of with five different estimation methods: uniformly minimum variance unbiased(UMVU), maximum likelihood(ML), least squares(LS), weighted least squares (WLS) and percentile(PC) estimators are considered. The performance of these estimation procedures, based on the mean squared error (MSE) by numerical simulations are compared. Simulation studies express that the UMVU estimator performs better than others and when the sample size is large enough the ML and UMVU estimators are almost equivalent and efficient than LS, WLS and PC. Finally, the result using a real data set are analyzed.

scholarly journals Outlier Detection Algorithms Over Fuzzy Data with Weighted Least Squares

2021 ◽  
Author(s):  
Natalia Nikolova ◽  
Rosa M. Rodríguez ◽  
Mark Symes ◽  
Daniela Toneva ◽  
Krasimir Kolev ◽  
...  
Keyword(s):  
Least Squares ◽  
Outlier Detection ◽  
Weighted Least Squares ◽  
Fuzzy Data ◽  
Detection Algorithms
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