Modeling of input–output relationships for a plasma spray coating process using soft computing tools

Abstract

To automate any manufacturing process, its input–output relationships are to be known in both forward and reverse directions. The present work aims to correlate input process parameters with various responses of a plasma spray coating process. Statistical regression analysis had been carried out previously for this process based on the data collected through central composite design of experiments to establish input–output relationships in forward direction. However, the said relationships could not be accurately determined in reverse direction using the obtained regression equations due to the presence of a non-square transformation matrix. Soft computing-based approaches had been developed to model the process in both forward as well as reverse directions. The performances of the developed approaches had been tested on different cases obtained through real experiments. A comparative study had been made of these developed approaches in terms of accuracy in predictions.

Introduction

Plasma spray coating process is an effective surface engineering technique for its good thermal protectiveness, high hardness and wear resistance. The process covers a wide range of industrial applications including manufacturing, textile, and paper industries, and so on. An atmospheric plasma spraying is governed by a number of parameters in order to get desired products. Plasma spray coating process does not have any robust mathematical formulation or model, which can be used to predict its input–output relationships.

Researchers across the globe showed immense interest to model the process efficiently. Attempts had been made to capture the dynamics of the process. Plasma spraying is such a complicated process comprising of various phenomena, that it might not be always possible to develop an appropriate differential equation to represent its input–output relationships. In such situations, models are generally made from the outcomes of experiments performed according to some statistical designs and then, analyzed using regression methods to predict the required outputs. The regression equations can be either linear or non-linear. Several investigators tried to model thermal spraying processes using statistical regression techniques. Saravanan et al. [1] carried out experimental investigations to produce high-quality alumina coatings by optimizing the detonation spray process parameters following a (L16-24) factorial design approach. Mawdsley et al. [2] conducted statistically designed experiments and multiple regression analysis to determine the effects of process parameters on three properties of plasma sprayed alumina coatings, namely permeability, hardness and thickness. The parameters, viz., powder injection angle, powder injection offset, plasma gun power, plasma gas flow, percent of hydrogen in plasma gas flow and spray distance had been used in 2-level fractional factorial design of experiments; and the parameters, namely carrier gas flow, spray distance, power and plasma gas flow had been considered in 3-level D-optimal design of experiments. A factorial design of experiments was utilized by Jandin and his associates [3] to analyze the correlation between operating conditions, microstructure and mechanical properties of twin wire arc sprayed steel coatings. Li et al. [4] investigated plasma sprayed titanium-nitride coatings using a uniform design method. Again, Li et al. [5] used a uniform design of experiments for optimizing the plasma spray process parameters of yttria stabilized zirconia coatings. The third-order regression equations obtained from their analysis were the most appropriate ones to identify the influence of process parameters. A D-optimal experimental design had been used by Azarmi et al. [6] to characterize the effects of atmospheric plasma spray process parameters on in-flight particle temperature and velocity, and on the oxide content and porosity in a nickel-based super-alloy coating. Wang and Coyle [7] performed the optimization of solution precursor plasma spray process through a small central composite design, which investigated the effects of six process parameters on coating porosity and deposition efficiency.

Soft computing-based tools are other potential techniques to capture the non-linearity involved in the plasma spraying process. In the recent past, Duan and his associates [8] attempted to use fuzzy logic-based model to show the effects of operating parameters of an argon/helium plasma spray process on the properties. Guessasma et al. [9] had been working on the implementations of neural network-based approaches in plasma spraying process. They designed expert system using neural networks to control the plasma spray process. Modeling of the atmospheric plasma spray process including parameter optimization and property prediction had been done using multilayer perceptrons [10]. Guessasma and Coddet analyzed the microstructure of plasma sprayed alumina–titania coatings using artificial neural network [11]. They applied neural computation to atmospheric plasma spray process for porosity analysis [12] also. Neural network model had been implemented to predict the rate of coating deposition under various operational conditions by Chaithanya et al. [13]. Wear characteristics of alumina–titania coatings had been analyzed using neural computation [14], [15]. Back-propagation neural network had been implemented by Wang et al. [16] to investigate temperature and velocity distribution regularities of in-flight particles; and build up the nonlinear relationship between spray parameters and coating porosity, hardness. Artificial neural networks had also been applied by Kanta et al. [17] to predict atmospheric plasma process parameters required in order to deposit a coating with the desired structural characteristics.

Manufacturing processes having highly non-linearity and strongly coupled characteristics could be modeled using radial basis functions neural network (RBFNN). Several techniques had been developed by various investigators for structure optimization of the RBFNN. An adaptive Gaussian radial basis functions neural network (GaRBFNN) was used by Tay and Butler [18] to approximate the stochastically non-linear dynamics of a metal inert gas (MIG) welding process in order to optimize some basic parameters. Their scheme had been applied to static parameter settings only. Tan et al. [19] proposed two learning algorithms for the parametric RBFNN developed using the stochastic gradient descent method and an unsupervised clustering method. Leung et al. [20] applied a GA to obtain optimum radial basis function (RBF) parameters. Zhu and He [21] used fuzzy C-means algorithm to obtain the centers and widths of the Gaussian functions utilized in the hidden layer of RBFNN, and the connecting weights were updated using a gradient descent algorithm. It is important to mention that the performance of RBFNN could be dependent on the number and nature of the obtained clusters. Peng et al. [22] proposed a method for simultaneous network structure determination and parameter optimization on the continuous space. Staiano et al. [23] described a novel approach to improve RBF network performance in regression tasks by means of a supervised fuzzy clustering. Amarnath and Pratihar [24] solved forward and reverse mapping problems of tungsten inert gas welding process using RBFNNs.

The input–output relationships of a process in both forward as well as reverse directions are essential to automate the same. This study aims to develop various neural network-based approaches for the predictions of outputs (in forward mapping) and inputs (in reverse mapping) of a plasma spray coating process.

The remaining part of this paper is organized as follows: Section 2 describes the experimental details and data collection methods adopted in the present study. Results of statistical regression analysis also have been depicted in this section. The developed approaches are discussed in Section 3. Results are stated and discussed in Section 4. Some concluding remarks are made in Section 5, and Section 6 describes the scopes for future study.