# Smoothing by cubic spline modified applied to solve inverse thermal problem

## Abstract

This paper presents an alternative to cubic spline regularization and its weighted form applied in solving inverse thermal problems. The inverse heat transfer problems are classified as ill-posed, that is, the solution may become unstable, mainly because they are sensitive to random errors deriving from the input data, necessitating a regularization method to soften these effects. The smoothing technique proposed by cubic spline regularization ensures that the global data tend to be more stable, with fewer data oscillations and dependent on a single arbitrary parameter input. It also shows that the weighted cubic spline is able to enhance filter action. The methods have been implemented in order for the search engine to optimize the choice of parameters and weight and, thus, the smoothing gains more flexibility and accuracy. The simulated and experimental tests confirm that the techniques are effective in reducing the amplified noise by inverse thermal problem presented.

- Authors:

- University of São Paulo State, UNESP, Department of Biological Sciences, Faculty of Sciences and Letters of Assis FCLA (Brazil)

- Publication Date:

- OSTI Identifier:
- 22769359

- Resource Type:
- Journal Article

- Journal Name:
- Computational and Applied Mathematics

- Additional Journal Information:
- Journal Volume: 37; Journal Issue: 2; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; ERRORS; HEAT TRANSFER; MATHEMATICAL SOLUTIONS; NOISE; RANDOMNESS; SIMULATION

### Citation Formats

```
Kubo, Leticia Hiromi, E-mail: leticiahk@assis.unesp.br, and Oliveira, Juliana de, E-mail: juliana@assis.unesp.br.
```*Smoothing by cubic spline modified applied to solve inverse thermal problem*. United States: N. p., 2018.
Web. doi:10.1007/S40314-016-0385-X.

```
Kubo, Leticia Hiromi, E-mail: leticiahk@assis.unesp.br, & Oliveira, Juliana de, E-mail: juliana@assis.unesp.br.
```*Smoothing by cubic spline modified applied to solve inverse thermal problem*. United States. doi:10.1007/S40314-016-0385-X.

```
Kubo, Leticia Hiromi, E-mail: leticiahk@assis.unesp.br, and Oliveira, Juliana de, E-mail: juliana@assis.unesp.br. Tue .
"Smoothing by cubic spline modified applied to solve inverse thermal problem". United States. doi:10.1007/S40314-016-0385-X.
```

```
@article{osti_22769359,
```

title = {Smoothing by cubic spline modified applied to solve inverse thermal problem},

author = {Kubo, Leticia Hiromi, E-mail: leticiahk@assis.unesp.br and Oliveira, Juliana de, E-mail: juliana@assis.unesp.br},

abstractNote = {This paper presents an alternative to cubic spline regularization and its weighted form applied in solving inverse thermal problems. The inverse heat transfer problems are classified as ill-posed, that is, the solution may become unstable, mainly because they are sensitive to random errors deriving from the input data, necessitating a regularization method to soften these effects. The smoothing technique proposed by cubic spline regularization ensures that the global data tend to be more stable, with fewer data oscillations and dependent on a single arbitrary parameter input. It also shows that the weighted cubic spline is able to enhance filter action. The methods have been implemented in order for the search engine to optimize the choice of parameters and weight and, thus, the smoothing gains more flexibility and accuracy. The simulated and experimental tests confirm that the techniques are effective in reducing the amplified noise by inverse thermal problem presented.},

doi = {10.1007/S40314-016-0385-X},

journal = {Computational and Applied Mathematics},

issn = {0101-8205},

number = 2,

volume = 37,

place = {United States},

year = {2018},

month = {5}

}