scholarly journals Two-stage segment linearization as part of the thermocouple measurement chain

2021 ◽  
Vol 54 (1-2) ◽  
pp. 141-151
Author(s):  
Dragan Živanović ◽  
Milan Simić
Keyword(s):  
Transfer Functions ◽  
Approximation Error ◽  
Linearization Method ◽  
Linear Segment ◽  
Virtual Instrumentation ◽  
Memory Consumption ◽  
Thermocouple Measurement ◽  
Two Stage ◽  
Approximation Errors ◽  
Input Range

An implementation of a two-stage piece-wise linearization method for reduction of the thermocouple approximation error is presented in the paper. First, the whole thermocouple measurement chain of a transducer is described, and possible error is analysed to define the required level of accuracy for linearization of the transfer characteristics. Evaluation of linearization functions and analysis of approximation errors are performed by the virtual instrumentation software package LabVIEW. The method is appropriate for thermocouples and other sensors where nonlinearity varies a lot over the range of input values. The basic principle of this method is to first transform the abscissa of the transfer function by a linear segment look-up table in such a way that significantly nonlinear parts of the input range are expanded before a standard piece-wise linearization. In this way, applying equal-segment linearization two times has a similar effect to non-equal-segment linearization. For a given examples of the thermocouple transfer functions, the suggested method provides significantly better reduction of the approximation error, than the standard segment linearization, with equal memory consumption for look-up tables. The simple software implementation of this two-stage linearization method allows it to be applied in low calculation power microcontroller measurement transducers, as a replacement of the standard piece-wise linear approximation method.

scholarly journals Transformed Structural Properties Method to Determine the Controllability and Observability of Robots

2021 ◽  
Vol 11 (7) ◽  
pp. 3082
Author(s):  
Dany Ivan Martinez ◽  
José de Jesús Rubio ◽  
Victor Garcia ◽  
Tomas Miguel Vargas ◽  
Marco Antonio Islas ◽  
...  
Keyword(s):  
Structural Properties ◽  
Approximation Error ◽  
Linearization Method ◽  
Controllability And Observability ◽  
Better Than

Many investigations use a linearization method, and others use a structural properties method to determine the controllability and observability of robots. In this study, we propose a transformed structural properties method to determine the controllability and observability of robots, which is the combination of the linearization and the structural properties methods. The proposed method uses a transformation in the robot model to obtain a linear robot model with the gravity terms and uses the linearization of the gravity terms to obtain the linear robot model; this linear robot model is used to determine controllability and observability. The described combination evades the structural conditions requirement and decreases the approximation error. The proposed method is better than previous methods because the proposed method can obtain more precise controllability and observability results. The modified structural properties method is compared with the linearization method to determine the controllability and observability of three robots.

scholarly journals A two-stage calibration method for industrial robots with joint and drive flexibilities

2015 ◽  
Vol 6 (2) ◽  
pp. 191-201 ◽  
Author(s):  
M. Neubauer ◽  
H. Gattringer ◽  
A. Müller ◽  
A. Steinhauser ◽  
W. Höbarth
Keyword(s):  
Transfer Functions ◽  
Geometric Model ◽  
Maximum Error ◽  
Industrial Robots ◽  
Robot Calibration ◽  
Two Stage ◽  
End Effector ◽  
The Real ◽  
Frequency Responses ◽  
Real Robot

Abstract. Dealing with robot calibration the neglection of joint and drive flexibilities limit the achievable positioning accuracy significantly. This problem is addressed in this paper. A two stage procedure is presented where elastic deflections are considered for the calculation of the geometric parameters. In the first stage, the unknown stiffness and damping parameters are identified. To this end the model based transfer functions of the linearized system are fitted to captured frequency responses of the real robot. The real frequency responses are determined by exciting the system with periodic multisine signals in the motor torques. In the second stage, the identified elasticity parameters in combination with the measurements of the motor positions are used to compute the real robot pose. On the basis of the estimated pose the geometric calibration is performed and the error between the estimated end-effector position and the real position measured with an external sensor (laser-tracker) is minimized. In the geometric model, joint offsets, axes misalignment, length errors and gear backlash are considered and identified. Experimental results are presented, where a maximum end-effector error (accuracy) of 0.32 mm and for 90 % of the poses a maximum error of 0.23 mm was determined (Stäubli TX90L).

Approximation Model for Radiation Impedance of a Square Piston Source on an Infinite Planar Baffle

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
John Valacas
Keyword(s):  
Transfer Functions ◽  
Approximation Error ◽  
Dimensionless Frequency ◽  
Approximation Model ◽  
Model Accuracy ◽  
Radiation Impedance ◽  
Wide Range ◽  
Finite Sum ◽  
Infinite Planar ◽  
Better Than

Abstract Approximation models based on a finite sum of Bessel functions of the first kind and a pair of simple rational transfer functions are proposed for radiation resistance and reactance of a square piston source mounted on an infinite planar baffle. Model accuracy is better than 1.6% for reactance and 0.5% for resistance within a very wide range of dimensionless frequency k√S (0.1–100). The very low and high frequency behaviors of radiation impedance are incorporated into the models' closed-form expressions so that the approximation error outside the specified frequency range tends to zero.

On the K-functional in learning theory

2019 ◽  
Vol 18 (03) ◽  
pp. 423-446
Author(s):  
Bao-Huai Sheng ◽  
Jian-Li Wang
Keyword(s):  
Learning Theory ◽  
Reproducing Kernel ◽  
Reproducing Kernel Hilbert Space ◽  
Approximation Error ◽  
Translation Operator ◽  
Modulus Of Smoothness ◽  
Generalized Translation Operator ◽  
Generalized Translation ◽  
Approximation Errors ◽  
Derivatives Of

[Formula: see text]-functionals are used in learning theory literature to study approximation errors in kernel-based regularization schemes. In this paper, we study the approximation error and [Formula: see text]-functionals in [Formula: see text] spaces with [Formula: see text]. To this end, we give a new viewpoint for a reproducing kernel Hilbert space (RKHS) from a fractional derivative and treat powers of the induced integral operator as fractional derivatives of various orders. Then a generalized translation operator is defined by Fourier multipliers, with which a generalized modulus of smoothness is defined. Some general strong equivalent relations between the moduli of smoothness and the [Formula: see text]-functionals are established. As applications, some strong equivalent relations between these two families of quantities on the unit sphere and the unit ball are provided explicitly.

Two-Stage Piece-Wise Linearization Method

2004 ◽  
Vol 24 (2) ◽  
Author(s):  
Ď.B. Zivanoví ◽  
M.Z. Arsí ◽  
J.R. Djordjevic
Keyword(s):  
Linearization Method ◽  
Two Stage

Optimization of the Neural Network by Using the LabVIEW Instrumentation

2012 ◽  
Vol 463-464 ◽  
pp. 1011-1016 ◽  
Author(s):  
Adrian Olaru ◽  
Serban Olaru ◽  
Dan Paune ◽  
Oprean Aurel
Keyword(s):  
Neural Network ◽  
Transfer Functions ◽  
Error Function ◽  
Virtual Instrumentation ◽  
Closed Loops ◽  
Network Parameters ◽  
The Neural Network ◽  
On Line ◽  
The Mean ◽  
Number Of Iterations

The paper shown one assisted method to construct simple and complex neural network and to simulate on-line them. By on-line simulation of some more important neural simple and complex network is possible to know what will be the influences of all network parameters like the input data, weight, biases matrix, sensitive functions, closed loops and delay of time. There are shown some important neurons type, transfer functions, weights and biases of neurons, and some complex layers with different type of neurons. By using the proper virtual LabVIEW instrumentation in on-line using, were established some influences of the network parameters to the number of iterations before canceled the mean square error to the target. Numerical simulation used the proper teaching law and proper virtual instrumentation. In the optimization step of the research on used the minimization of the error function between the output and the target.

Complexity issues for the symmetric interval eigenvalue problem

2014 ◽  
Vol 13 (1) ◽  
Author(s):  
Milan Hladík
Keyword(s):  
Computational Complexity ◽  
Eigenvalue Problem ◽  
Relative Error ◽  
Symmetric Matrix ◽  
Approximation Error ◽  
Np Hard ◽  
Approximation Errors ◽  
The Matrix ◽  
Polynomially Solvable ◽  
Relative Approximation

AbstractWe study the problem of computing the maximal and minimal possible eigenvalues of a symmetric matrix when the matrix entries vary within compact intervals. In particular, we focus on computational complexity of determining these extremal eigenvalues with some approximation error. Besides the classical absolute and relative approximation errors, which turn out not to be suitable for this problem, we adapt a less known one related to the relative error, and also propose a novel approximation error. We show in which error factors the problem is polynomially solvable and in which factors it becomes NP-hard.

scholarly journals An adaptive two-stage analog/regression model for probabilistic prediction of small-scale precipitation in France

2018 ◽  
Vol 22 (1) ◽  
pp. 265-286 ◽  
Author(s):  
Jérémy Chardon ◽  
Benoit Hingray ◽  
Anne-Catherine Favre
Keyword(s):  
Regression Model ◽  
Large Scale ◽  
Linear Models ◽  
Transfer Functions ◽  
Small Scale ◽  
Probabilistic Prediction ◽  
Two Stage ◽  
Precipitation Occurrence ◽  
Seasonal Stratification ◽  
Local Weather

Abstract. Statistical downscaling models (SDMs) are often used to produce local weather scenarios from large-scale atmospheric information. SDMs include transfer functions which are based on a statistical link identified from observations between local weather and a set of large-scale predictors. As physical processes driving surface weather vary in time, the most relevant predictors and the regression link are likely to vary in time too. This is well known for precipitation for instance and the link is thus often estimated after some seasonal stratification of the data. In this study, we present a two-stage analog/regression model where the regression link is estimated from atmospheric analogs of the current prediction day. Atmospheric analogs are identified from fields of geopotential heights at 1000 and 500 hPa. For the regression stage, two generalized linear models are further used to model the probability of precipitation occurrence and the distribution of non-zero precipitation amounts, respectively. The two-stage model is evaluated for the probabilistic prediction of small-scale precipitation over France. It noticeably improves the skill of the prediction for both precipitation occurrence and amount. As the analog days vary from one prediction day to another, the atmospheric predictors selected in the regression stage and the value of the corresponding regression coefficients can vary from one prediction day to another. The model allows thus for a day-to-day adaptive and tailored downscaling. It can also reveal specific predictors for peculiar and non-frequent weather configurations.

A two stage DC/dc converter with wide input range for EV

2014 ◽  
Author(s):  
Peng Wen ◽  
Changsheng Hu ◽  
Haitao Yang ◽  
Longlong Zhang ◽  
Cheng Deng ◽  
...  
Keyword(s):  
Two Stage ◽  
Input Range

scholarly journals The Log-Linear Return Approximation, Bubbles, and Predictability

2012 ◽  
Vol 47 (3) ◽  
pp. 643-665 ◽  
Author(s):  
Tom Engsted ◽  
Thomas Q. Pedersen ◽  
Carsten Tanggaard
Keyword(s):  
Stock Returns ◽  
Upper Bound ◽  
Approximation Error ◽  
Expected Returns ◽  
Price Ratio ◽  
Rational Bubbles ◽  
Large Samples ◽  
Approximation Errors ◽  
The Mean ◽  
Log Linear

AbstractWe study in detail the log-linear return approximation introduced by Campbell and Shiller (1988a). First, we derive an upper bound for the mean approximation error, given stationarity of the log dividend-price ratio. Next, we simulate various rational bubbles that have explosive conditional expectation, and we investigate the magnitude of the approximation error in those cases. We find that, surprisingly, the Campbell-Shiller approximation is very accurate even in the presence of large explosive bubbles. Only in very large samples do we find evidence that bubbles generate large approximation errors. Finally, we show that a bubble model in which expected returns are constant can explain the predictability of stock returns from the dividend-price ratio that many previous studies have documented.

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