An estimation method of fractal parameters on rough surfaces based on the exact spectral moment using artificial neural network

Kai Jiang, Zhifeng Liu, Yang Tian, Tao Zhang and Congbin Yang

Chaos, Solitons & Fractals, 2022, vol. 161, issue C

Abstract: Fractal parameters (FP) significantly influence contact mechanics characteristics, such as contact stiffness, friction and wear. The existing methods liking the power spectral density (PSD), structure function (SF), autocorrelation function (ACF), box-counting (Box) and roughness length (RMS) methods are limited by the identification accuracy of FP (fractal dimension D and fractal roughness G). These methods are not suitable for global D interval (Kulesza et al., 2014; Feng et al., 2018), thereby resulting in large estimation errors (error (D) exceeds 40 %, and the value of G is incorrect). Thus, in this paper, a neural network FP estimation method based on the exact spectral moment is proposed. The main contribution of this paper is to establish the mapping relationship between the exact spectral moment and FP through the neural network. Firstly, the exact spectral moments, m0, m2 and m4, are derived via the differentiability of the series Weierstrass-Mandelbrot (WM) function in the finite interval. Secondly, a series of spectral moment parameter correspondence tables are generated according to the provided ideal fractal parameters. Then, the spectral moment is taken as the input layer and fractal parameters as the output layer, after which the BP neural network is optimized using the NSGA-II algorithm. Moreover, the mapping relationship between the FP and the spectral moment is established, thus obtaining the Fractal parameters estimation neural network (FPENN). The FP estimation model is trained by a relatively large amount of data and packaged to form a brand-new FP estimation method. Finally, the effectiveness of the proposed method is demonstrated by comparison with the existing methods. The results show that the relative error of D is <0.1 %, and the relative error of G is <25 %.

Keywords: Surface topography; Spectral moment; FP identification; Neural network (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077922005768
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922005768

DOI: 10.1016/j.chaos.2022.112366

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().