A non-linear method for the calculation of the loss tangent distribution function

1996 ◽  
Vol 35 (4) ◽  
pp. 315-320 ◽  
Author(s):  
C. L. Matteo ◽  
S. Cerveny
Keyword(s):  
Distribution Function ◽  
Loss Tangent ◽  
Linear Method ◽  
Non Linear ◽  
Tangent Distribution

A non-linear theory for a full cavitating hydrofoil in a transverse gravity field

1967 ◽  
Vol 29 (2) ◽  
pp. 317-336 ◽  
Author(s):  
Bruce E. Larock ◽  
Robert L. Street
Keyword(s):  
Gravity Field ◽  
Linear Theory ◽  
Mixed Boundary ◽  
Linear Method ◽  
Two Dimensional ◽  
Mixed Boundary Value Problem ◽  
Cavity Model ◽  
Cavity Size ◽  
Non Linear ◽  
Cavitating Hydrofoil

An analysis is made of the effect of a transverse gravity field on a two-dimensional fully cavitating flow past a flat-plate hydrofoil. Under the assumption that the flow is both irrotational and incompressible, a non-linear method is developed by using conformal mapping and the solution to a mixed-boundary-value problem in an auxiliary half plane. A new cavity model, proposed by Tulin (1964a), is employed. The solution to the gravity-affected case was found by iteration; the non-gravity solution was used as the initial trial of a rapidly convergent process. The theory indicates that the lift and cavity size are reduced by the gravity field. Typical results are presented and compared to Parkin's (1957) linear theory.

The response matrix acceleration: A new non-linear method for the 3D discrete-ordinate transport equation

2020 ◽  
Vol 146 ◽  
pp. 107642
Author(s):  
Wesley Ford ◽  
Emiliano Masiello ◽  
Christophe Calvin ◽  
François Févotte ◽  
Bruno Lathuilière
Keyword(s):  
Transport Equation ◽  
Linear Method ◽  
Response Matrix ◽  
Discrete Ordinate ◽  
Non Linear

scholarly journals Modeling Bidirectional Polarization Distribution Function of Land Surfaces Using Machine Learning Techniques

2020 ◽  
Vol 12 (23) ◽  
pp. 3891
Author(s):  
Siyuan Liu ◽  
Yi Lin ◽  
Lei Yan ◽  
Bin Yang
Keyword(s):  
Machine Learning ◽  
Remote Sensing ◽  
Distribution Function ◽  
Accurate Estimation ◽  
Polarization Distribution ◽  
Scattering Angle ◽  
Non Linear ◽  
Linear Problems ◽  
Input Variables ◽  
Land Surfaces

Accurate estimation of polarized reflectance (Rp) of land surfaces is critical for remote sensing of aerosol optical properties. In the last two decades, many data-driven bidirectional polarization distribution function (BPDF) models have been proposed for accurate estimation of Rp, among which the generalized regression neural network (GRNN) based BPDF model has been reported to perform the best. GRNN is just a simple machine learning (ML) technique that can solve non-linear problems. Many ML techniques were reported to work well in solving non-linear problems and consequently may provide better performance in BPDF modeling. However, incorporating various ML techniques with BPDF modeling and comparing their performances have never been well documented. In this study, three widely used ML algorithms—i.e., support vector regression (SVR), K-nearest-neighbor (KNN), and random forest (RF)—were applied for BPDF modeling. Using measurements collected by the Polarization and Directionality of the Earth’s Reflectance onboard PARASOL satellite (POLDER/PARASOL), non-linear relationships between Rp and the input variables, i.e., Fresnel factor (Fp), scattering angle (SA), reflectance at 670 nm (R670) and 865 nm (R865), were built using these ML algorithms. Results showed that taking Fp, SA, R670, and R865 as input variables, the performance of the four ML-based BPDF models was quite similar. The KNN-based BPDF model provided slightly better results, and improved the accuracy of the semi-empirical BPDF models by 9.55% in terms of the overall root mean square error (RMSE). Experiments of different configuration of input variables suggested that using multi-band reflectance as input variables provided better results than using vegetation indices. The RF-based BPDF model using all reflectances at six bands as input variables produced the best results, improving the overall accuracy by 6.62% compared with the GRNN-based BPDF model. Among all the input variables, reflectance at absorbing spectral bands—e.g., 490 nm and 670 nm—played more significant roles in RF-based BPDF modeling due to the domination of polarized partition in total reflectance. Fresnel factor and scattering angle were also important for BPDF modeling. This study confirmed the feasibility of applying ML techniques to more accurate BPDF modeling, and the RF-based BPDF model proposed in this study can be used to increase the accuracy of remote sensing of the complete aerosol properties.

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