Empirical Similarity Analysis Using Adaptive Trigonometric Functions

2009 ◽  
Author(s):  
Srikanth Tadepalli ◽  
Kristin L. Wood
Keyword(s):  
Experimental Data ◽  
Error Analysis ◽  
Complex Systems ◽  
Drag Coefficient ◽  
Engineering Design ◽  
Numerical Algorithms ◽  
Similarity Analysis ◽  
Trigonometric Functions ◽  
Numerical Approximations ◽  
Prediction Parameters

Similarity methods have been widely employed in engineering design and analysis to model and scale complex systems. The Empirical Similitude Method (ESM) is one such method based on the use of experimental data. Using a variant of the similitude process involving experimental data, we present in this paper, the use of advanced numerical approximations, trigonometric functions in particular to model and predict the performance of design artifacts. Specifically, an airfoil design is modeled, and the values of the drag coefficient are estimated based on the advanced ESM. Intermediate test specimens are used to correlate experimental data to produce the required prediction parameters. Mathematical development and error analysis are also elaborated by delving into continuity and adaptivity features of numerical algorithms.

scholarly journals Applying Computer Algebra Systems in Approximating the Trigonometric Functions

2018 ◽  
Vol 23 (3) ◽  
pp. 37 ◽  
Author(s):  
Le Quan ◽  
Thái Nhan
Keyword(s):  
Error Analysis ◽  
Computer Algebra ◽  
Numerical Algorithms ◽  
High Accuracy ◽  
Computer Algebra Systems ◽  
Trigonometric Functions ◽  
Modern Computer ◽  
Sine And Cosine Functions ◽  
Cosine Functions ◽  
Very High

We propose numerical algorithms which can be integrated with modern computer algebra systems in a way that is easily implemented to approximate the sine and cosine functions with an arbitrary accuracy. Our approach is based on Taylor’s expansion about a point having a form of kp, k∈Z and p=π/2, and being chosen such that it is closest to the argument. A full error analysis, which takes advantage of current computer algebra systems in approximating π with a very high accuracy, of our proposed methods is provided. A numerical integration application is performed to demonstrate the use of algorithms. Numerical and graphical results are implemented by MAPLE.

scholarly journals A Note on the Perturbation of arithmetic expressions

2016 ◽  
Vol 13 (1) ◽  
pp. 190-197
Author(s):  
Baghdad Science Journal
Keyword(s):  
Error Analysis ◽  
Gaussian Elimination ◽  
Effective Means ◽  
Numerical Algorithms ◽  
Posteriori Error ◽  
Condition Numbers ◽  
A Posteriori ◽  
Rounding Errors ◽  
A Posteriori Error ◽  
Forward Error

In this paper we present the theoretical foundation of forward error analysis of numerical algorithms under;• Approximations in "built-in" functions.• Rounding errors in arithmetic floating-point operations.• Perturbations of data.The error analysis is based on linearization method. The fundamental tools of the forward error analysis are system of linear absolute and relative a prior and a posteriori error equations and associated condition numbers constituting optimal of possible cumulative round – off errors. The condition numbers enable simple general, quantitative bounds definitions of numerical stability. The theoretical results have been applied a Gaussian elimination, and have proved to be very effective means of both a priori and a posteriori error analysis.

Rule of Thumb Modelling of Biofilm Reactors

1990 ◽  
Vol 22 (1-2) ◽  
pp. 405-418 ◽  
Author(s):  
S. Elmaleh
Keyword(s):  
Experimental Data ◽  
Computer Simulation ◽  
Complex Systems ◽  
Flow Pattern ◽  
Zero Order ◽  
Design Tool ◽  
Rule Of Thumb ◽  
Biofilm Reactors ◽  
Number Of Species ◽  
Operational Variables

Biofilm reactors are very complex systems, the modelling of which requires sophisticated kinetic relationships concerning the highest number of species in reaction and computer simulation. In fact, the process engineer needs a rule of thumb method able to predict the output variables after modification of the operational variables. Such a “simplissime” model is derived by considering a plate reactor coated with a biofilm through which the substrates are diffusion transported and eliminated with a zero order intrinsic reaction. When the liquid-biofilm resistance is neglected, conversion depends on one parameter only, the meaning of which can be displayed. Moreover, in many cases, the flow pattern influence can be neglected. This “simplissime” model was shown accurate enough in fitting various experimental data and it can even be used as a design tool.

scholarly journals Fractional-Derivative Approximation of Relaxation in Complex Systems

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Kin M. Li ◽  
Mihir Sen ◽  
Arturo Pacheco-Vega
Keyword(s):  
Differential Equation ◽  
Experimental Data ◽  
System Identification ◽  
Complex Systems ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Order Differential Equation ◽  
Initial Conditions ◽  
Time Dependent ◽  
Fractional Order Differential Equation

In this paper, we present a system identification (SI) procedure that enables building linear time-dependent fractional-order differential equation (FDE) models able to accurately describe time-dependent behavior of complex systems. The parameters in the models are the order of the equation, the coefficients in it, and, when necessary, the initial conditions. The Caputo definition of the fractional derivative, and the Mittag-Leffler function, is used to obtain the corresponding solutions. Since the set of parameters for the model and its initial conditions are nonunique, and there are small but significant differences in the predictions from the possible models thus obtained, the SI operation is carried out via global regression of an error-cost function by a simulated annealing optimization algorithm. The SI approach is assessed by considering previously published experimental data from a shell-and-tube heat exchanger and a recently constructed multiroom building test bed. The results show that the proposed model is reliable within the interpolation domain but cannot be used with confidence for predictions outside this region. However, the proposed system identification methodology is robust and can be used to derive accurate and compact models from experimental data. In addition, given a functional form of a fractional-order differential equation model, as new data become available, the SI technique can be used to expand the region of reliability of the resulting model.

Combined analytical and experimental approaches to rotor components stress predictions

2011 ◽  
Vol 225 (4) ◽  
pp. 322-330 ◽  
Author(s):  
M Chierichetti ◽  
C McColl ◽  
D Palmer ◽  
M Ruzzene ◽  
O Bauchau
Keyword(s):  
Experimental Data ◽  
Dynamic Response ◽  
Complex Systems ◽  
Rotor Blade ◽  
Experimental Approach ◽  
Numerical Results ◽  
Multibody Model ◽  
Lab Experiments ◽  
Experimental Approaches ◽  
Thin Walled

A combined analytical and experimental approach is introduced to estimate the dynamic response of complex systems from a limited number of measurements. The method is based on the concept that modal information is sufficient to extrapolate the complete map of the response from experimental data through the reconstruction of modal loads. The capabilities of the algorithm are first verified via well-controlled lab experiments on a thin-walled aluminium-rotor blade. Numerical results from a comprehensive UH-60 multibody model are then compared with available experimental data. Significant improvements in the accuracy of the predicted results are achieved when simple airloads models are employed as inputs.

Computational Simulations of Vertebral Body for Optimal Instrumentation Design

2012 ◽  
Vol 6 (2) ◽  
Author(s):  
F. Casesnoves
Keyword(s):  
Experimental Data ◽  
Engineering Design ◽  
Vertebral Body ◽  
Technical Difficulty ◽  
Regions Of Interest ◽  
Computational Method ◽  
Mechanical Forces ◽  
Computational Simulations ◽  
Large Sets ◽  
Fitting Model

The engineering design of surgical instrumentation to exert forces and torques/moments on bones during operations constitutes a rather difficult task. This technical difficulty is caused mainly by the natural, pathological, and individual irregularities of the human bone morphologies and surfaces. Usually, mechanical forces are applied on determined parts of bone surfaces, so-called regions of interest (ROIs). We describe a computational method (CAD) to digitalize, simulate, and fit mathematically the anterior vertebral body morphometric. Based on experimental data from 17 cadaveric specimens, large sets of surface digital points were generated. Complete anterior vertebral body morphologies were visualized and analyzed with subroutines, which are initially used to select these natural ROIs. Subsequently, an optimized fitting model was implemented for the ROIs. 3D surface equations of the anterior vertebral body (L3, L4, L5, and S1) were determined. Statistics and determination coefficients which define the error boundaries and goodness of the model, were calculated and mathematically analyzed. A bioengineering application is the use of these equations for the industrial design of an innovative vertebral distractor. The device separates two adjacent vertebrae in parallel, and minimizes the force to carry out the surgical maneuver.

Study on the Minimum Drag Coefficient Phenomenon of Supercritical Pressure Water in the Pseudocritical Region

2012 ◽  
Author(s):  
Xianliang Lei ◽  
Huixiong Li ◽  
Shuiqing Yu ◽  
Yifan Zhang ◽  
Tingkuan Chen
Keyword(s):  
Experimental Data ◽  
Pressure Drop ◽  
Drag Coefficient ◽  
Supercritical Pressure ◽  
Pressure Drops ◽  
Minimum Drag ◽  
Wide Range ◽  
Pressure Water ◽  
Isothermal Flows ◽  
Supercritical Pressure Water

With the development of supercritical (and even ultra-supercritical) pressure boilers (SCBs) with high capacities, and at the same time, with the consideration of supercritical pressure water-cooled reactors (SCWRs) as one of the six most promising reactor concepts accepted in the Generation IV International Forum (GIF), flow and heat transfer of supercritical water becomes more and more important for both the design and operation safety of the related facilities. Thermo-hydraulic characteristics are among the issues, which are of special significance for the SCBs and SCWRs. It has been found that at supercritical pressures, the hydraulic resistance of water exhibits special characteristics in regions near its pseudo-critical point, which is hereafter called the minimum drag coefficient phenomenon. Experimental investigation was carried out in the present study to investigate further the characteristics of drag coefficient of supercritical pressure water under different conditions. The total pressure drop characteristic of water flowing in smooth tube and internally ribbed tube under the supercritical pressures was measured in experiments with a wide range of operational parameters, such as the system pressures ranging from 23 to 28 MPa, the average heat fluxes varied from 100 kW/m2 to 500kW/m2, and the mass fluxes of water in a range of 600 ∼ 1050 kg/m2s. The experimental data were compared with prediction results calculated by existing common correlations for single phase pressure drops, and large discrepancies were observed between the experimental data and the prediction results. Furthermore, the pressure drops characteristics of supercritical pressure water in cases with different tube arrangement and test conditions were compared with each other, such as that in horizontal tubes and vertical tubes, and that in isothermal flows and in non-isothermal flows. Additionally, this phenomenon observed in the present studies was also analyzed by using computational fluid dynamics technology, and the mechanism of pressure drop variation was reasonably explained. It was found that the deviation appeared between the previously proposed drag coefficient correlations and the present experimental data was mainly owning to ignoring the variation of an existence of the minimum drag coefficient in the pseudo critical region in previous studies, and based on the data obtained in this study, a new correlation for drag coefficient for supercritical pressure water was presented.

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