scholarly journals Rotational invariance conditions in elasticity, gradient elasticity and its connection to isotropy

2016 ◽  
Vol 23 (1) ◽  
pp. 3-42 ◽  
Author(s):  
Ingo Münch ◽  
Patrizio Neff
Keyword(s):  
Linear Model ◽  
Linear Models ◽  
Gradient Elasticity ◽  
Invariance Condition ◽  
Interesting Point ◽  
Finite Rotations ◽  
Linear Gradient ◽  
Frame Indifference ◽  
New Variant ◽  
Variational Formulations

For homogeneous higher-gradient elasticity models we discuss frame-indifference and isotropy requirements. To this end, we introduce the notions of local versus global SO(3)-invariance and identify frame-indifference (traditionally) with global left SO(3)-invariance and isotropy with global right SO(3)-invariance. For specific restricted representations, the energy may also be local left SO(3)-invariant as well as local right SO(3)-invariant. Then we turn to linear models and consider a consequence of frame-indifference together with isotropy in nonlinear elasticity and apply this joint invariance condition to some specific linear models. The interesting point is the appearance of finite rotations in transformations of a geometrically linear model. It is shown that when starting with a linear model defined already in the infinitesimal symmetric strain [Formula: see text], the new invariance condition is equivalent to the isotropy of the linear formulation. Therefore, it may also be used in higher-gradient elasticity models for a simple check of isotropy and for extensions to anisotropy. In this respect we consider in more detail variational formulations of the linear indeterminate couple-stress model, a new variant of it with symmetric force stresses and general linear gradient elasticity.

scholarly journals Analysis of a Linear Model for Non-Synchronous Vibrations Near Stall

2021 ◽  
Vol 6 (3) ◽  
pp. 26
Author(s):  
Christoph Brandstetter ◽  
Sina Stapelfeldt
Keyword(s):  
Linear Model ◽  
Linear Models ◽  
Structural Vibration ◽  
Experimental Investigations ◽  
Vibration Modes ◽  
Critical Problem ◽  
Safety Critical ◽  
Unstable Vibration ◽  
Aero Engines ◽  
Lock In

Non-synchronous vibrations arising near the stall boundary of compressors are a recurring and potentially safety-critical problem in modern aero-engines. Recent numerical and experimental investigations have shown that these vibrations are caused by the lock-in of circumferentially convected aerodynamic disturbances and structural vibration modes, and that it is possible to predict unstable vibration modes using coupled linear models. This paper aims to further investigate non-synchronous vibrations by casting a reduced model for NSV in the frequency domain and analysing stability for a range of parameters. It is shown how, and why, under certain conditions linear models are able to capture a phenomenon, which has traditionally been associated with aerodynamic non-linearities. The formulation clearly highlights the differences between convective non-synchronous vibrations and flutter and identifies the modifications necessary to make quantitative predictions.

scholarly journals A Cascaded Unsupervised Model for PoS Tagging

2021 ◽  
Vol 20 (1) ◽  
pp. 1-23
Author(s):  
Necva Bölücü ◽  
Burcu Can
Keyword(s):  
Linear Model ◽  
Language Processing ◽  
Bayesian Model ◽  
Linear Models ◽  
Syntactic Category ◽  
Semantic Parsing ◽  
Pos Tagging ◽  
Part Of Speech ◽  
Sentence Level ◽  
Log Linear

Part of speech (PoS) tagging is one of the fundamental syntactic tasks in Natural Language Processing, as it assigns a syntactic category to each word within a given sentence or context (such as noun, verb, adjective, etc.). Those syntactic categories could be used to further analyze the sentence-level syntax (e.g., dependency parsing) and thereby extract the meaning of the sentence (e.g., semantic parsing). Various methods have been proposed for learning PoS tags in an unsupervised setting without using any annotated corpora. One of the widely used methods for the tagging problem is log-linear models. Initialization of the parameters in a log-linear model is very crucial for the inference. Different initialization techniques have been used so far. In this work, we present a log-linear model for PoS tagging that uses another fully unsupervised Bayesian model to initialize the parameters of the model in a cascaded framework. Therefore, we transfer some knowledge between two different unsupervised models to leverage the PoS tagging results, where a log-linear model benefits from a Bayesian model’s expertise. We present results for Turkish as a morphologically rich language and for English as a comparably morphologically poor language in a fully unsupervised framework. The results show that our framework outperforms other unsupervised models proposed for PoS tagging.

scholarly journals Linear power-flow analysis method for AC-DC electric power networks

2021 ◽  
Author(s):  
Mohammadreza Vatani
Keyword(s):  
Power Systems ◽  
Linear Model ◽  
Power Flow ◽  
Linear Models ◽  
Power Converters ◽  
Power Balance ◽  
Balance Equations ◽  
Dc Power ◽  
Phase Angles ◽  
Dc Power Systems

AC-DC power systems have been operating more than sixty years. Nonlinear bus-wise power balance equations provide accurate model of AC-DC power systems. However, optimization tools for planning and operation require linear version, even if approximate, for creating tractable algorithms, considering modern elements such as DERs (distributed energy resources). Hitherto, linear models of only AC power systems are available, which coincidentally are called DC power flow. To address this drawback, linear bus-wise power balance equations are developed for AC-DC power systems and presented. As a first contribution, while AC and DC lines are represented by susceptance and conductance elements, AC-DC power converters are represented by a proposed linear relationship. As a second contribution, a three-step linear AC-DC power flow method is proposed. The first step solves the whole network considering it as a linear AC network, yielding bus phase angles at all busses. The second step computes attributes of the proposed linear model of all AC-DC power converters. The third step solves the linear model of the AC-DC system including converters, yielding bus phase angles at AC busses and voltage magnitudes at DC busses. The benefit of the proposed linear power flow model of AC-DC power system, while an approximation of the nonlinear model, enables representation of bus-wise power balance of AC-DC systems in complex planning and operational optimization formulations and hence holds the promise of phenomenal progress. The proposed linear AC-DC power systems is tested on numerous IEEE test systems and demonstrated to be fast, reliable, and consistent.

scholarly journals Experimental validation of wind energy estimation

2020 ◽  
Vol 24 (6 Part A) ◽  
pp. 3795-3806
Author(s):  
Predrag Zivkovic ◽  
Mladen Tomic ◽  
Vukman Bakic
Keyword(s):  
Wind Speed ◽  
Linear Model ◽  
Linear Models ◽  
Stokes Equations ◽  
Momentum Conservation ◽  
Electricity Production ◽  
Navier Stokes ◽  
Energy Estimation ◽  
Navier Stokes Equations ◽  
Non Linear

Wind power assessment in complex terrain is a very demanding task. Modeling wind conditions with standard linear models does not sufficiently reproduce wind conditions in complex terrains, especially on leeward sides of terrain slopes, primarily due to the vorticity. A more complex non-linear model, based on Reynolds averaged Navier-Stokes equations has been used. Turbulence was modeled by modified two-equations k-? model for neutral atmospheric boundary-layer conditions, written in general curvelinear non-orthogonal co-ordinate system. The full set of mass and momentum conservation equations as well as turbulence model equations are numerically solved, using the as CFD technique. A comparison of the application of linear model and non-linear model is presented. Considerable discrepancies of estimated wind speed have been obtained using linear and non-linear models. Statistics of annual electricity production vary up to 30% of the model site. Even anemometer measurements directly at a wind turbine?s site do not necessarily deliver the results needed for prediction calculations, as extrapolations of wind speed to hub height is tricky. The results of the simulation are compared by means of the turbine type, quality and quantity of the wind data and capacity factor. Finally, the comparison of the estimated results with the measured data at 10, 30, and 50 m is shown.

scholarly journals A linear model for leaf area measurement to screen potential leaf material for herbal drug in Adhatoda vasica L.

2016 ◽  
Vol 8 (1) ◽  
pp. 140-143
Author(s):  
J. V. Thaker ◽  
R. P. Kuvad ◽  
V. S. Thaker
Keyword(s):  
Water Content ◽  
Leaf Area ◽  
Linear Model ◽  
Plant Species ◽  
Linear Models ◽  
Dry Weight ◽  
Nondestructive Method ◽  
Area Measurement ◽  
Adhatoda Vasica ◽  
Linear Correlations

Leaf area is an important parameter in physiology and agronomy studies. Linear models for leaf area measurement are developed for plant species as a nondestructive method. The plant Adhatoda vasica L. (a medicinal plant) was selected and the leaves of this plant were used for development of linear model for leaf area using Leaf Area Meter (LAM) software. Planimetric parameters (length, length2, width and width2) and gravimetric (dry weight and water content) parameters are considered for the development of linear model for this plant species. Single factor ANOVA and linear correlations were worked out using these parameters and leaf area. The plant was showed significant relationship with the parameters studied. The best correlation as represented by regression coefficient (R2) was used and improved R2 is worked out. It is observed that with increase in leaf area, water content is also increased and showed best correlation with the leaf area. Thus water content can be taken as a parameter for developing linear model for leaf area is concluded.

scholarly journals The Application of Log-Linear Model to Selected Poison Patients

2020 ◽  
pp. 1-7
Author(s):  
Fatin N.S.A. ◽  
Norlida M.N. ◽  
Siti Z.M.J.
Keyword(s):  
Linear Model ◽  
Linear Models ◽  
Demographic Data ◽  
Contingency Tables ◽  
Categorical Variables ◽  
State Variables ◽  
Exposure Route ◽  
Higher Dimensional ◽  
Route Of Exposure ◽  
Log Linear

Log-linear model is a technique used to analyze the cross-classification categorical data or the contingency table. It is used to obtain the parsimony models that describe the interaction between the categorical variables in contingency tables. Log-linear models are commonly used in evaluating higher dimensional contingency tables that involves more than two categorical variables. This study focuses on analyzing data of poisoned patients from 2012 to 2014 using log-linear model. There are two model analyzed; model for demographic data of patients and model of poisoning information. For the first model, the variables involved are gender, age, race and state. Variables for the second model are circumstance of exposure, type of exposure, location of exposure, route of exposure and types of poison. Both log-linear models are developed to investigate the association between variables in the model. As a result of this study, the best model for demographic data and poisoning information are the model with three-ways interaction. For the best model of demographic data, there is an association between gender, age and race, race, gender and state as well as age, race and state. Meanwhile, the best model for poisoning information reveals that there is relationship between circumstance of exposure, route of exposure and type of poison, location of exposure, route of exposure and type of poison, circumstance of exposure, type of exposure and route of exposure, circumstance of exposure, location of exposure and route of exposure, circumstance of exposure, type of exposure and type of poison and also type of exposure, location of exposure and type of poison. Keywords: log-linear; demographic; gender; age; race; state; circumstance of exposure; type of exposure; location of exposure; route of exposure; types of poison

scholarly journals Sensitivity of the General Linear Model to Assumptions

2020 ◽  
Vol 6 (5) ◽  
pp. 21-25
Keyword(s):  
Linear Model ◽  
Gaussian Noise ◽  
Linear Models ◽  
General Linear Model ◽  
White Gaussian Noise ◽  
General Linear ◽  
Optimal Estimator ◽  
Significant Performance ◽  
Non Gaussian ◽  
Noise Models

Non-Gaussian noise often causes in significant performance abatement for systems which are designed using Gaussian assumption. This report challenges the question of General Linear Model with White Gaussian Noise assumption in order to define the sensitivity of the performance of an optimal estimator. Gaussian noise models provide an important role in many signal processing applications. The Laplacian and Uniform signal are two worthy examples of noise that can be compared to the White Gaussian Noise, though the sensitivity which can be compared with any non-Gaussian. White Gaussian Noise has been considered for General Linear Models and deviation from whiteness would affect on our estimates under different circumstances. Moreover, new assumptions have been considered to generate different type of signals in order to evaluate the sensitivity of the General Linear Model.

scholarly journals Hybrid MARMA-NARX model for flow forecasting based on the large-scale climate signals, sea-surface temperatures, and rainfall

2018 ◽  
Vol 49 (6) ◽  
pp. 1788-1803 ◽  
Author(s):  
Mohammad Ebrahim Banihabib ◽  
Arezoo Ahmadian ◽  
Mohammad Valipour
Keyword(s):  
Linear Model ◽  
Hybrid Model ◽  
Large Scale ◽  
Linear Models ◽  
Moving Average ◽  
Effective Parameters ◽  
Forecasting Accuracy ◽  
Local Factor ◽  
Non Linear ◽  
Climate Signals

Abstract In this study, to reflect the effect of large-scale climate signals on runoff, these indices are accompanied with rainfall (the most effective local factor in runoff) as the inputs of the hybrid model. Where one-year in advance forecasting of reservoir inflows can provide data to have an optimal reservoir operation, reports show we still need more accurate models which include all effective parameters to have more forecasting accuracy than traditional linear models (ARMA and ARIMA). Thus, hybridization of models was employed for improving the accuracy of flow forecasting. Moreover, various forecasters including large-scale climate signals were tested to promote forecasting. This paper focuses on testing MARMA-NARX hybrid model to enhance the accuracy of monthly inflow forecasts. Since the inflow in different periods of the year has in linear and non-linear trends, the hybrid model is proposed as a means of combining linear model, monthly autoregressive moving average (MARMA), and non-linear model, nonlinear autoregressive model with exogenous (NARX) inputs to upgrade the accuracy of flow forecasting. The results of the study showed enhanced forecasting accuracy through using the hybrid model.

Linear Dynamic Models

1999 ◽  
Author(s):  
Ronald K. Pearson
Keyword(s):  
Linear Model ◽  
Discrete Time ◽  
Continuous Time ◽  
Dynamic Models ◽  
Linear Models ◽  
Time Varying ◽  
Infinite Dimensional ◽  
Linear Dynamic ◽  
Time Invariant ◽  
Linear Dynamic Models

It was emphasized in Chapter 1 that low-order, linear time-invariant models provide the foundation for much intuition about dynamic phenomena in the real world. This chapter provides a brief review of the characteristics and behavior of linear models, beginning with these simple cases and then progressing to more complex examples where this intuition no longer holds: infinite-dimensional and time-varying linear models. In continuous time, infinite-dimensional linear models arise naturally from linear partial differential equations whereas in discrete time, infinite-dimensional linear models may be used to represent a variety of “slow decay” effects. Time-varying linear models are also extremely flexible: In the continuous-time case, many of the ordinary differential equations defining special functions (e.g., the equations defining Bessel functions) may be viewed as time-varying linear models; in the discrete case, the gamma function arises naturally as the solution of a time-varying difference equation. Sec. 2.1 gives a brief discussion of low-order, time-invariant linear dynamic models, using second-order examples to illustrate both the “typical” and “less typical” behavior that is possible for these models. One of the most powerful results of linear system theory is that any time-invariant linear dynamic system may be represented as either a moving average (i.e., convolution-type) model or an autoregressive one. Sec. 2.2 presents a short review of these ideas, which will serve to establish both notation and a certain amount of useful intuition for the discussion of NARMAX models presented in Chapter 4. Sec. 2.3 then briefly considers the problem of characterizing linear models, introducing four standard input sequences that are typical of those used in linear model characterization. These standard sequences are then used in subsequent chapters to illustrate differences between nonlinear model behavior and linear model behavior. Sec. 2.4 provides a brief introduction to infinite-dimensional linear systems, including both continuous-time and discrete-time examples. Sec. 2.5 provides a similar introduction to the subject of time-varying linear systems, emphasizing the flexibility of this class. Finally, Sec. 2.6 briefly considers the nature of linearity, presenting some results that may be used to define useful classes of nonlinear models.

scholarly journals Generalized Born radii computation using linear models and neural networks

2019 ◽  
Vol 36 (6) ◽  
pp. 1757-1764
Author(s):  
Saida Saad Mohamed Mahmoud ◽  
Gennaro Esposito ◽  
Giuseppe Serra ◽  
Federico Fogolari
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Linear Model ◽  
Correlation Coefficient ◽  
Linear Models ◽  
Reference Method ◽  
Supplementary Information ◽  
Model Parameters ◽  
Generalized Born ◽  
Supplementary Material

Abstract Motivation Implicit solvent models play an important role in describing the thermodynamics and the dynamics of biomolecular systems. Key to an efficient use of these models is the computation of generalized Born (GB) radii, which is accomplished by algorithms based on the electrostatics of inhomogeneous dielectric media. The speed and accuracy of such computations are still an issue especially for their intensive use in classical molecular dynamics. Here, we propose an alternative approach that encodes the physics of the phenomena and the chemical structure of the molecules in model parameters which are learned from examples. Results GB radii have been computed using (i) a linear model and (ii) a neural network. The input is the element, the histogram of counts of neighbouring atoms, divided by atom element, within 16 Å. Linear models are ca. 8 times faster than the most widely used reference method and the accuracy is higher with correlation coefficient with the inverse of ‘perfect’ GB radii of 0.94 versus 0.80 of the reference method. Neural networks further improve the accuracy of the predictions with correlation coefficient with ‘perfect’ GB radii of 0.97 and ca. 20% smaller root mean square error. Availability and implementation We provide a C program implementing the computation using the linear model, including the coefficients appropriate for the set of Bondi radii, as Supplementary Material. We also provide a Python implementation of the neural network model with parameter and example files in the Supplementary Material as well. Supplementary information Supplementary data are available at Bioinformatics online.

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