Multivariate interpolation

Multivariate interpolation refers to the process of estimating the values of a multivariable function at points within a multidimensional space using discrete datasets obtained from experimental results or numerical calculations. This is done by constructing an interpolation function that approximates the behavior of the function on a given grid. Multivariate interpolation is necessary when the function cannot be expressed in algebraic form due to its complexity.From: Numerical Methods for Engineers and Scientists [2019], Optimization for the minimum fuel consumption problem of a hybrid electric vehicle using mixed-integer linear programming [2023]

Mechanics and Electromagnetics

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Published in Sergey Edward Lyshevski, Mechatronics and Control of Electromechanical Systems, 2017

Sergey Edward Lyshevski

Note: The polynomial and spline interpolants can be applied. We use physics-consistent rational, trigonometric, and exponential functions. The nonlinear trigonometric polynomials and mixed trigonometric-exponential interpolations are physics-consistent. Frequently, one solves the bicubic, trilinear (three variable), and multivariate interpolation problems. For example, the viscous friction may be a multivariate function, Tfriction = f(ωr, TLoad, TTemperature).

Optimization for the minimum fuel consumption problem of a hybrid electric vehicle using mixed-integer linear programming

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Published in Engineering Optimization, 2023

Gentaro Yamanaka, Masakatsu Kuroishi, Tadayoshi Matsumori

The nonlinear terms emerging in the constraints can be classified into two types. The first type includes bilinear terms, such as , which is the product of and . In addition, if or R are considered the design variables, or are also regarded as bilinear terms. The second type includes nonlinear multivariate functions, such as , , and . Multivariable functions are difficult to express in algebraic form and are therefore expressed using a multivariate interpolation from discrete datasets on any grid based on experimental results or numerical calculations.

Multivariate interpolation

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Mechanics and Electromagnetics

Optimization for the minimum fuel consumption problem of a hybrid electric vehicle using mixed-integer linear programming