Methods For Calculation Of Derivatives Research Articles

An Adaptable Fault Current Derivative Calculation Method for Derivative Relays in HVDC Grids

This paper presents an adaptable method for fault current derivative calculation in high voltage direct current (HVDC) grids composed of modular multilevel converters (MMCs). The proposed method can be used for current derivative calculation under different fault scenarios including pole-to-pole, pole-to-ground, and pole-to-metallic. The proposed method is adaptable as it can provide accurate fault current derivatives in various grid topologies such as symmetric monopole, asymmetric monopole with ground or metallic return, and bipole with ground or metallic return, as well as grids with different types of converters with and without fault-blocking capability including full-bridge MMCs (FB-MMCs), half-bridge MMCs (HB-MMCs), or a mix of HB- and FB-MMCs. The paper also demonstrates how the proposed current derivative calculation method can be used to form a derivative relay, which is fast, selective, computationally efficient, and insensitive to fault resistance. Furthermore, using the proposed current derivative calculation method, all relay settings are analytically calculated instead of being obtained through time-consuming simulation studies. Simulation results for various fault scenarios, grid topologies, and converter configurations show that the calculation method is accurate and the presented relaying algorithm can detect various faults within 10 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> s, even when the fault resistance is as high as 500 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Upomega$</tex-math></inline-formula> .

Структура и особенности программного комплекса для геофизических геометрических 3D-инверсий

The structure and features of a software package for 3D inversion of geophysical data are considered. The presented software package is focused on solving direct and inverse problems of electrical exploration and engineering geophysics. In addition to the parameters that determine physical properties of the medium, the software package allows you to restore the geometry parameters of the geophysical model, namely layer reliefs and boundaries of three-dimensional inclusions. The inclusions can be in the form of arbitrary hexagons or prisms with a polygonal base. The software package consists of four main subsystems: an interface, subsystems for solving direct and inverse problems, and a client-server part for performing calculations on remote computing nodes. The graphical interface consists of geophysicist-oriented pre- and postprocessor modules that allow you to describe the problem and present the results of its solution in user-friendly terms. To solve direct problems, the finite element method and the technology for dividing the field into normal and anomalous components are used. At the same time, special methods of discretization of the computational domain are used, which make it possible to take into account both the complex three-dimensional structure of the environment and the presence of man-made objects (wells) in the computational domain. To increase the efficiency of solving direct problems, nonconforming grids with cells in the form of arbitrary hexahedrons are used. Methods for efficient calculation of derivatives (with respect to these parameters) necessary for solving inverse problems by the Gauss-Newton method are also described for the geometry parameters. The main idea for efficient derivatives computation is to identify the effect of changing the value of the parameter (used to compute the value of the generalized derivative) on the problem. The main actions performed by the subsystem for solving inverse problems and the features associated with the processing of geometry parameters are described.

A New Aerodynamic Optimization Method with the Consideration of Dynamic Stability

Dynamic stability is significantly important for flying quality evaluation and control system design of the advanced aircraft, and it should be considered in the initial aerodynamic design process. However, most of the conventional aerodynamic optimizations only focus on static performances and the dynamic motion has never been included. In this study, a new optimization method considering both dynamic stability and general lift-to-drag ratio performance has been developed. First, the longitudinal combined dynamic derivative based on the small amplitude oscillation method is calculated. Then, combined with the PSO (particle swarm optimization) algorithm, a dynamic stability derivative that must not be decreased is added to the constraints of optimization and the lift-drag ratio is chosen as the optimization objective. Finally, a new aerodynamic optimization method can be built. We take NACA0012 as an example to validate this method. The results show that the dynamic derivative calculation method is effective and conventional optimization design can significantly improve the lift-drag ratio. However, the dynamic stability is enormously changed at the same time. By contrast, the new optimization method can improve the lift-drag performance while maintaining the dynamic stability.

A hybrid onboard adaptive model for aero-engine parameter prediction

An onboard aero-engine model with low computation burden and high accuracy is urgent for online parameter prediction in some model-based control applications. However, current engine models, including component level models, linear models and data-driven models cannot meet the demands of model-based control and diagnostics well. Thus, a novel hybrid adaptive model is proposed, which consists of a component level model, an improved incremental linearized Kalman filter and a state space model. The improved linearized Kalman filter is used to adapt the component level model to the performance degradations of the engine, and the state space model is implemented for online prediction with a low computation burden. Both the linearized Kalman filter and the state space model are obtained by linearizing the adaptive component level model in real-time. Thus, an exact derivative calculation method is extended and an improved transient calculation and linearization joint algorithm is proposed to achieve real-time property. Experiments are conducted to demonstrate the effectiveness and real-time property of proposed model in terms of estimation accuracy, prediction accuracy and time consumption. The results show that the proposed adaptive model can not only estimate the health parameters and track the performance degradations well but also predict interesting outputs over next several sample periods accurately and quickly. In addition, the proposed adaptive model can complete the estimation and prediction task in a sample period (25 ms) in a micro-controller unit, which suggests the great real-time property of the proposed model.

A new online modelling method for aircraft engine state space model

To overcome the drawbacks of current modelling method for aircraft engine state space model, a new method is introduced. The form of state space model is derived by using Talyor series to expand the nonlinear model that is implicit equations and involves many iterations. A partial derivative calculation method for iterations is developed to handle the influence of iterations on parameters. The derivative calculation and the aerothermodynamics calculations are combined in the component level model with fixed number Newton-Raphson (N-R) iterations. Mathematical derivation and simulations show the convergence ability of proposed method. Simulations show that comparing with the linear parameter varying model and centered difference based state space model, much higher accuracy of proposed online modelling method is achieved. The accuracy of the state space model built by proposed method can be maintained when the step amplitudes of inputs are within 2%, and the responses of the state space model can match those of the component level model when each input steps larger amplitudes. In addition, an online verification was carried out to show the capability of modelling at any operating point and that state space model can predict future outputs accurately. Thus, the effectiveness of the proposed method is demonstrated.

A numerical method to compute derivatives of functions of large complex matrices and its application to the overlap Dirac operator at finite chemical potential

We present a method for the numerical calculation of derivatives of functions of general complex matrices. The method can be used in combination with any algorithm that evaluates or approximates the desired matrix function, in particular with implicit Krylov–Ritz-type approximations. An important use case for the method is the evaluation of the overlap Dirac operator in lattice Quantum Chromodynamics (QCD) at finite chemical potential, which requires the application of the sign function of a non-Hermitian matrix to some source vector. While the sign function of non-Hermitian matrices in practice cannot be efficiently approximated with source-independent polynomials or rational functions, sufficiently good approximating polynomials can still be constructed for each particular source vector. Our method allows for an efficient calculation of the derivatives of such implicit approximations with respect to the gauge field or other external parameters, which is necessary for the calculation of conserved lattice currents or the fermionic force in Hybrid Monte-Carlo or Langevin simulations. We also give an explicit deflation prescription for the case when one knows several eigenvalues and eigenvectors of the matrix being the argument of the differentiated function. We test the method for the two-sided Lanczos approximation of the finite-density overlap Dirac operator on realistic SU(3) gauge field configurations on lattices with sizes as large as 14×143 and 6×183.

Research Progress and Prospects for Vehicle Dynamic Stability Parameters

Dynamic stability parameters (dynamic derivatives) are important indicators for the control system design, orbit design and longitudinal and horizontal dynamic stability analysis of aircrafts. Methods that evaluate the quality and dynamics of an aircraft typically include flight experiment, wind tunnel testing and theoretical calculation, with one of the most important part of them being the obtainment of dynamic derivatives. Project estimation method derivative action is not considered suitable for boundary layer transition, flow separation and re-attached and the complex situation leeward area vortex small angle of attack linear range. Frequency domain is a dynamic non-scheduled periodic invariant system to get moving derivative calculation method, but the accuracy of the unsteady flow is much lower than the time-domain calculations. Currently, unsteady CFD approach represents a time-domain nonlinear aerodynamic characteristics predicted the most advanced level. Derivative prediction efficiency and adaptability under conditions of high angle of attack of the development trend of nonlinear dynamic derivatives were analyzed. As a global trend, obtaining dynamic parameters through numerical calculation is becoming a prevailing approach to dynamic parameter research.

Fast and robust computation of Cartesian derivatives of Zernike polynomials

This work deals with a problem of an effective and robust evaluation of Cartesian partial derivatives of Zernike polynomials. Calculations based on explicit relations suffer from high computational costs and are numerically instable for higher orders. Thus, fast and numerically stable methods for calculation of derivatives of Zernike polynomials are needed. Such methods employing recursive techniques based on the relation of Zernike radial polynomials to Jacobi polynomials are proposed. The performance of proposed algorithms is compared to the standard calculation using explicit relations.

Compensation for the intrinsic dynamics of the InMotion2 robot

The InMotion2 and other similarly designed robots, are commonly used for rehabilitation of neurological injuries and motor adaptation studies. These robots are used to simulate haptic environments; however, anisotropy in end-point impedance due to the intrinsic robot dynamics can compromise these experiments. The goal was to decrease the magnitude and anisotropy of the robot impedance using a dynamic compensation algorithm that reduces the forces normally felt by the user during rapid movements. We tested this algorithm with two different methods for real-time calculation of derivatives, a novel quadratic fit method (CQF) and the commonly used backward derivative method (CBD). Six subjects performed a series of point-to-point movements under three conditions (no compensation, CQF, CBD), in different directions at peak speeds of 50, 100 and 150cm/s. Without compensation, tangential peak-to-peak forces were as large as 69N in certain directions at the 150cm/s speed. Both CQF and CBD significantly reduced tangential forces in all directions and speeds. CQF outperformed CBD in the directions with highest intrinsic impedance, reducing tangential forces by 64% in these directions. Compensation also significantly reduced forces normal to the movement direction, with CQF again outperforming CBD in several cases. Anisotropy was assessed by the range of tangential peak-to-peak forces across movement directions. In the no compensation condition, anisotropy was as high as 52.7N at the 150cm/s speed, but an average anisotropy reduction of 74% was achieved with CQF. The CQF method can significantly reduce impedance and anisotropy in this class of robot.

STUDY OF LOCAL THERMAL NONEQUILIBRIUM IN POROUS MEDIA DUE TO TEMPERATURE SUDDEN CHANGE AND HEAT GENERATION

In this paper we examine the effects of temperature sudden change in boundary x = 0 and great heat generating on the creation of local thermal nonequilibrium (LTNE) in the semiinfinite stagnant porous media. Two energy equations in the transient state and in the presence of heat generating are used as the governing equations in each phase. These partial governing equations solve numerically. For partial derivatives, we use from Compact finite difference method that is the continuous method for calculation of derivatives and for progress in time, we use from RK4. So we test values of heat transfer rate for early and late times using perturbation and shooting methods. Rate of heat transfer between phases depict in the figures. Results show that effects of heat generating and LTNE are restrained at very late times and graphs slope decrease to zero. In this time, the temperature gradient moves towards the infinite with a constant value. Also, effect of different nondimension parameters on behavior of temperature gradients is verified. When diffusivity ratio a increases, time to counteract heat generation effect increases. Fluid and solid graphs are stabilized in the negative value of tem-perature gradient with the constant slop zero and different diffusivity ratios a don't affect on this value. So for a &gt; 1, the difference between solid and fluid phases will increase and vice versa, for a &lt; 1 it will decrease.Heat generation effect is counteracted in earlier times when conductivity ratio y increases. So The graphs state that when y increases, the value of the difference de-creases and temperature gradient of the phases are more&nbsp;coinciding and Contact point of the phases tend to earlier time. Other characterizations are explained in detailed.http://dx.doi.org/10.5755/j01.mech.17.1.204

Seismic modeling by the spectral-finite difference method

The paper presents several efficient algorithms based on the combination of the spectral method for calculation of derivatives with respect to one or two spatial coordinates with a 1D finite difference approximation with respect to the remaining spatial coordinate and time. A few types of algorithms are discussed depending on the behavior of elastic parameters. We also propose an algorithm for the reduced problem based on the use of the finite difference approximation only with respect to the spatial coordinate. In this case the obtained system of ordinary differential equations with respect to time reduces to N independent Cauchy problems by means of the matrix decomposition method. The latter problems are analytically solved. Some examples of calculation of synthetic seismograms for different models are given.

Raman and NIR Spectroscopic Methods for Determination of Total Dietary Fiber in Cereal Foods: A Comparative Study

Partial least-squares regression (PLSR) was used to generate three Raman and three near-infrared reflectance (NIRR) models for the spectroscopic determination of total dietary fiber (TDF) of a wide variety of cereal foods. To allow comparison of the spectral techniques, both analyses used the same sets of samples ( ncal = 63, nval = 63). Six models were optimized by full leave-one-out cross-validation (CV), including a smoothed, a first-, and a second-derivative model for each spectral technique. Both kinds of raw spectral data required correction of interfering baseline and amplitude variations. Derivative preprocessing generally reduced the number of latent variables (LVs) for both spectral types and significantly reduced the CV error of the Raman models. The derivative treatments enhanced the influence of select vibrational-bandwidth-sized features in the Raman data (64–84 cm−1). The Savitzky–Golay derivative calculation method was better for the NIRR data, while the gap-difference method was better for the Raman data, which had a higher level of baseline noise. Raman models required 6 to 9 latent variables while NIRR models required 10 to 14 LVs. The root-mean-squared CV model errors were 2–2.3% TDF for all six models, and the three Raman models had root-mean-squared prediction errors (RMSEPs) in the range 2.8–3.2% TDF, with the best model being generated from second-derivative data. First-derivative data provided the best NIRR model, and for all three NIRR models the RMSEP spanned 2.4–2.9%. For some types of samples, it is suggested that the Raman method is limited by its sampling technique and could be improved with more densely packed, larger-area specimens. The regression vectors of the Raman models seem more easily interpretable than NIRR models. Either spectral method appears capable of acheiving an acceptable level of error; TDF reference method precision was 0.68% TDF, while the product label information had an error of 2.8% TDF relative to the reference.

Numerical experiments with the pseudospectral method in spherical coordinates

Abstract A series of numerical experiments has been carried out to test the usefulness of the pseudospectral method for calculation of derivatives in spherical coordinates. The results indicate that the method is more accurate than a fourth‐order finite‐difference scheme for the same resolution, but the two methods are of comparable efficiency. Certain aspects of the filtering problems arising in numerical models are exposed and discussed.