How to Perform a Statistical Analysis of Non-Destructive Degradation Data to Study Crack Growth in Wind Blades as a Function of the Number of Cycles

Abstract

Objective: The aim of this paper is to show the application of the Exponential Regression Model to study the failure time of a system over time. The data was taken from the paper (Wang et al., 2021).   Theoretical framework: The linear regression model, where the response is associated with the explanatory variables by means of a linear model, is the best known. To formulate the model, it is necessary to specify a deterministic component and a random (stochastic) component. The exponential model should be used when it is assumed that risk is constant over time. Once the model has been specified, its parameters are estimated. In the absence of normal errors and especially in the presence of censoring, a more appropriate option is the maximum likelihood method. As the equations are non-linear in their parameters and do not have an analytical solution, it is necessary to use the Newton-Raphson numerical method. Due to the simplicity of the exponential regression model, few situations in practice are adequately adjusted by this model. The Weibull regression model is widely used in survival analysis (Bastos Lyra et al., 2008)   Method: Data taken from the article (Wang et al., 2021) e foi utilizado a Regressão Exponencial para modelar os dados.   Final Considerations: This result indicates that Exponential Regression is a very viable option when the aim is to monitor the number of cracks as a function of time to check whether a system will fail. In this specific Case Study, it is clear that one of the blades is better than the others and that there are some Probability Distribution models that are suitable for the model.   Implications of the research: The use cases of Exponential Regression are more restricted in the scientific literature and because of this, this case study is interesting to show that this model is effective for treating data in the area of reliability.   Originality/value: Despite being a well-known statistical tool, Exponential Regression has a specific application in monitoring the number of cracks over time in a system.