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Predictive Modelling of Critical Variables for Improving HVOF Coating using Gamma Regression Models

Wolfgang Rannetbauer, Simon Hubmer, Carina Hambrock, Ronny Ramlau

TL;DR

This paper addresses predicting HVOF coating properties by marrying a gamma regression GLM with a Central Composite Design (CCD) to efficiently explore the process space. It models non-negative, skewed responses with a Gamma distribution and a log link, estimating parameters via Maximum Likelihood Estimation and validating inference with Wald tests and AIC for model selection. Empirical results on eight coating-related responses demonstrate that reduced gamma-regression models often outperform full models, offering accurate predictions (via LOOCV) and actionable insights on influential factors such as Lambda and Total Gas Flow. The framework supports DOE-guided optimization of thermal spray processes and holds potential for extension with sensors and Bayesian GLMs to further boost predictive capabilities.

Abstract

Thermal spray coating is a critical process in many industries, involving the application of coatings to surfaces to enhance their functionality. This paper proposes a framework for modelling and predicting critical target variables in thermal spray coating processes, based on the application of statistical design of experiments (DoE) and the modelling of the data using generalized linear models (GLMs) with a particular emphasis on gamma regression. Experimental data obtained from thermal spray coating trials are used to validate the presented approach, demonstrating that it is able to accurately model and predict critical target variables. As such, the framework has significant potential for the optimization of thermal spray coating processes, and can contribute to the development of more efficient and effective coating technologies in various industries.

Predictive Modelling of Critical Variables for Improving HVOF Coating using Gamma Regression Models

TL;DR

This paper addresses predicting HVOF coating properties by marrying a gamma regression GLM with a Central Composite Design (CCD) to efficiently explore the process space. It models non-negative, skewed responses with a Gamma distribution and a log link, estimating parameters via Maximum Likelihood Estimation and validating inference with Wald tests and AIC for model selection. Empirical results on eight coating-related responses demonstrate that reduced gamma-regression models often outperform full models, offering accurate predictions (via LOOCV) and actionable insights on influential factors such as Lambda and Total Gas Flow. The framework supports DOE-guided optimization of thermal spray processes and holds potential for extension with sensors and Bayesian GLMs to further boost predictive capabilities.

Abstract

Thermal spray coating is a critical process in many industries, involving the application of coatings to surfaces to enhance their functionality. This paper proposes a framework for modelling and predicting critical target variables in thermal spray coating processes, based on the application of statistical design of experiments (DoE) and the modelling of the data using generalized linear models (GLMs) with a particular emphasis on gamma regression. Experimental data obtained from thermal spray coating trials are used to validate the presented approach, demonstrating that it is able to accurately model and predict critical target variables. As such, the framework has significant potential for the optimization of thermal spray coating processes, and can contribute to the development of more efficient and effective coating technologies in various industries.
Paper Structure (19 sections, 4 theorems, 37 equations, 7 figures, 7 tables)

This paper contains 19 sections, 4 theorems, 37 equations, 7 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Technical Background
  3. Predictive Modelling of hvof Coating Properties
  4. Generalized Linear Models (glms)
  5. Application of Generalized Linear Models to hvof Data
  6. The Gamma Distribution
  7. Maximum Likelihood Estimation Gamma Regression
  8. Numerical Computation of the Maximum Likelihood Estimator
  9. Asymptotic Properties of the Maximum Likelihood Estimator (mle)
  10. Linear Hypothesis Testing
  11. Model Selection Criteria
  12. Assessing Predictive Performance of hvof Coating Models
  13. Application to hvof Coating: Practical Implementation
  14. Central Composite Design
  15. Experimental Setup
  16. ...and 4 more sections

Key Result

Proposition 3.1

Let $\boldsymbol{s({\beta}| \mathbf{y})}$ represent the score function for a response vector $\mathbf{y}$, as defined in Definition score, and let $\mathbf{y}$ consist of observed values $y_i$ from a random variable $Y_i$ following a gamma distribution, as described in model. Then Here, $\mathbf{X} = (\mathbf{1}\ \mathbf{x})$ represents the design matrix, consisting of the explanatory variable $\

Figures (7)

  • Figure 2.1: Schematic depiction of the High Velocity Oxygen Fuel (hvof) process.
  • Figure 3.1: Comparison of gamma distributions with varied parameters. The left panel displays the probability density function (PDF) of a gamma-distributed random variable $y$ with a fixed shape parameter $a=5$ and varying rate parameters $b$. The right panel illustrates the PDF of a gamma-distributed random variable $y$ with a fixed rate parameter $b=2$ and varying shape parameters $a$.
  • Figure 5.1: Central Composite Design with a) $k=2$ factors and b) $k=3$ factors.
  • Figure 5.2: Illustration of the considered key factors in the HVOF coating process.
  • Figure 5.3: Photograph illustrating the experimental setup during the hvof coating process, showing the robot, turning lathe, and coating stream in action.
  • ...and 2 more figures

Theorems & Definitions (17)

  • Definition 3.1
  • Definition 3.2
  • Proposition 3.1
  • proof
  • Remark 3.1
  • Definition 3.3
  • Proposition 3.2
  • proof
  • Definition 3.4
  • Proposition 3.3: fahrmeir1985consistency
  • ...and 7 more