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Modeling of Thermal Systems
Published in Yogesh Jaluria, Design and Optimization of Thermal Systems, 2019
An important and valuable technique that is used extensively to represent the characteristics and behavior of components, materials, and systems is curve fitting. Results are obtained at a finite number of discrete points by numerical computation and/or experimentation. If these data are represented by means of a smooth curve, which passes through or as close as possible to the points, the equation of the curve can be used to obtain values at intermediate points where data are not available and also to model the characteristics of the system. Physical reasoning may be used in the choice of the type of curve employed for curve fitting, but the effort is largely a data-processing operation, unlike mathematical modeling, which is based on physical insight and experience. The equation obtained as a result of curve fitting then represents the performance of a given equipment or system and may be used in system simulation and optimization. This equation may also be employed in the selection of equipment such as blowers, compressors, and pumps from items readily available from manufacturers. Curve fitting is particularly useful in representing calibration results and material property data, such as the thermodynamic properties of a substance, in terms of equations that form part of the mathematical model of the system.
Curve Fitting and Interpolation
Published in Ramin S. Esfandiari, Numerical Methods for Engineers and Scientists Using MATLAB®, 2017
An available set of data can be used for different purposes. In some cases, the data is represented by a function, which in turn can be used for numerical differentiation or integration (Chapter 6). Such function may be obtained through curve fitting, or approximation, of the data. Curve fitting is a procedure where a function is used to fit a given set of data in the “best” possible manner without having to match the data exactly. As a result, while the function does not necessarily yield the exact value at the data points, overall it fits the set of data well. Several types of functions and polynomials of different degrees can be used for curve fitting purposes. Curve fitting is normally used when the data has substantial inherent error, such as data gathered from experimental measurements. The aforementioned function or polynomial can then be used for interpolation purposes; that is, to find estimates of values at intermediate points (points between the given data points) where the data is not directly available.
Graphical solutions
Published in Surinder S. Virdi, Advanced Construction Mathematics, 2019
Curve fitting is the process of finding equations of the curves which fit the given data. The method of least squares is a technique which avoids individual judgement in drawing lines, parabolas and other curves to fit the given data. If X and Y are the independent and the dependent variables, the quantity: D12 + D22 + ……….+ Dn2 must be minimum for a best fitting curve; see Figure 5.10.
A Novel Method of Curve Fitting Based on Optimized Extreme Learning Machine
Published in Applied Artificial Intelligence, 2020
Curve fitting is the process of finding a parameterized function that best matches a given set of data points. It can be viewed as a function approximation problem in such a way that a certain error measure must be addressed explicitly. Representing the data in a parameterized function or equation has actual significances in data analysis, visualization and computer graphics. Curve fitting can be served as aided tools for many techniques involved modeling and prediction. Particularly, scientists and engineers often notice that the best practice gaining some insight and guide to understand the related scientific phenomenon is to fit a set measured or observed data to an empirical relationship. From the resultant empirical formula, interpolation, extrapolation, differentiation, and finding the maximum or minimum location of the curve can be readily carried out without utilizing a full mathematical treatment based on the underlying theory. In addition, curve fitting is also frequently used to estimate the parameters in a variety of modeling studies. For example, the notch-delay solar model in the climate science has a number of independent parameters, which can be estimated by using a curve fitting method.
Alternative for the regionalization of flow duration curves
Published in Journal of Applied Water Engineering and Research, 2019
Raimunda da Silva e Silva, Claudio José Cavalcante Blanco, Francisco Carlos Lira Pessoa
Mimikou and Kaemaki (1985) developed a regionalization study of flow duration curves in western and northwestern Greece. Five mathematical models were used, namely, power, exponential, logarithmic, quadratic and cubic models for curve fitting. In the case of regionalization of curve parameters, the morphoclimatic characteristics of the basins, such as mean annual rainfall, drainage area, river head and length, were employed. In another case for prediction of FDC, the polynomial method fared better than the area-index regionalization method when applied on 15 ungauged catchments in Taiwan (Yu et al. 2002). Mazvimavi (2003) conducted a regional analysis study in 53 basins in Zimbabwe to estimate flow duration curves using the exponential model. Mamun et al. (2010) grouped similar low flow rate curves in the peninsular region of Malaysia and obtained regional maps and equations by multiple regression technique as a function of basin, mean annual rainfall and mean annual evaporation.
The role of socio-economic and property variables in the establishment of flood depth-damage curve for the data-scarce area in Malaysia
Published in Urban Water Journal, 2022
Sumiliana Sulong, Noor Suraya Romali
Curve fitting: Curve fitting is the process of constructing a mathematical function that best fits a series of data points (Pistrika, Tsakiris, and Nalbantis 2014). In the curve-plotting procedure uses empirical and synthetic damage data from the multivariate regression analysis model to perform the best-fitted curve. For the curve-fitting procedure, the value of the correlation coefficient, R-squared (R2), was used as a benchmark to best fit models (Amadio et al. 2019; Romali and Yusop 2021; Win et al. 2018). The damage factor equation from the best-fitted curve functions is established to facilitate flexibility in transferability to new areas and occurrences.