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Pulsed electrodeposition of Ni-W coatings predicts microhardness via gene expression programming

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Abstract

In the present work, a robust prediction model is presented for predicting Ni-W coating microhardness using powerful soft computing techniques, i.e., Gene expression programming (GEP). We considered the W content in coating (wt.%), pH, time (min) of coating bath, frequency (kHz) and current density (mA cm−2) of pulse current electrodeposition as input variables and the microhardness of Ni-W coatings as output variables. To achieve this, we had three main steps: (i) 63 experiments were collected to construct models; (ii) Creating training and testing phases based on 50 and 13 data and (iii) A new model is built and compared using correlation coefficients (R2), root relative square errors (RRSE), and relative standard errors (RSE). Using the results, GEP-6 was found to be the appropriate model for predicting the microhardness of Ni-W coatings with R2 = 0.9926, RSE = 0.0077, and RRSE = 0.0880. Additionally, sensitivity analysis results indicated that pulse electrodeposition's frequency, current density, and time of coating bath were the most effective parameters in determining microhardness.

Graphical abstract

Comparison of actual (experimented) versus predicted microhardness for Ni-W coatings using GEP-2, GEP-4, and GEP-6 models in (a) training, and (b) testing.

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Abbreviations

GEP:

Gene expression programming

RSE:

Relative standard error

MEMS:

Microelectromechanical systems

KMO:

Kaiser mayer olkin

PVD:

Physical vapor deposition

GA:

Genetic algorithm

CVD:

Chemical vapor deposition

GP:

Genetic programming

R2 :

Correlation coefficient

ET:

Expression tree

RRSE:

Root relative square error

SA:

Sensitivity analysis

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Authors and Affiliations

  1. Department of Materials Science and Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

    Z. Shojaei & G. R. Khayati

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  1. Z. Shojaei
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  2. G. R. Khayati
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Contributions

This research was performed by Mrs. Shojaei. Furthermore, Mrs. Shojaei was responsible for writing the manuscript. Also, Dr.Khayati acted as a supervisor in this research.

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Correspondence to Z. Shojaei.

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Shojaei, Z., Khayati, G.R. Pulsed electrodeposition of Ni-W coatings predicts microhardness via gene expression programming. J Appl Electrochem 53, 1433–1447 (2023). https://doi.org/10.1007/s10800-023-01844-9

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  • DOI: https://doi.org/10.1007/s10800-023-01844-9

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