PSI - Issue 38

Frédéric Kihm et al. / Procedia Structural Integrity 38 (2022) 12–29

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Kihm, Miu, Bonato / Structural Integrity Procedia 00 (2021) 000 – 000

In this paper, the fatigue damage from the strain gage measurements will be considered as one feature. It is calculated at regular time intervals. Fatigue damage is calculated from rainflow cycle counting the strain signal, and projecting the cycles ranges into a fatigue curve, which requires some material parameters (Bannantine (1990), Halfpenny (2001)). Engineers are usually familiar with fatigue calculations and their expertise is required to select the appropriate material parameters. In order for the various features to be comparable, it was decided to compute relative damage values from all the inputs. For example, a temperature could lead to some material expansion, which in turn can lead to strain or stress, so a temperature signal could be multiplied by a thermal expansion coefficient and then rainflow cycle counted to produce a relative damage metric. Similarly, an acceleration signal could be double integrated, so it becomes displacement of the point where the accelerometer is positioned, from which a relative damage value can be derived. This will produce a series of features, which will appear as columns as illustrated in Table 1.

Table 1. Illustration of the features used as input data for the following data exploration and model construction.

Time Interval

Damage_Accel1

Damage_Accel2

Damage_Temp1

Damage_Strain

1 2 3 4 5

1.23E-6 2.67E-6 5.24E-7 5.02E-6 3.16E-7

2.23E-6 3.23E-6 6.23E-7 7.23E-7 1.23E-6

2.23E-6 3.16E-7 6.23E-7 5.24E-7 2.67E-6

2.23E-6 3.23E-6 2.67E-6 7.23E-7 1.23E-6

…

…

…

…

…

2.4. Dimensionality reduction The next step is to evaluate if the dimension of the feature space can be reduced, by keeping only the relevant features. PCA (Principal Component Analysis) is commonly used for dimensionality reduction (James, Gareth, et al (2013)). PCA transforms the original independent variables into combinations of them to form the principal components of the data. The first principal component can equivalently be defined as a direction that maximizes the variance of the projected data. A given principal component can be taken as a direction orthogonal to the previous principal components that maximizes the variance of the projected data. The idea is to project each data point of the input data onto only the first few principal components to obtain lower-dimensional data while preserving as much of the variation in the data as possible. The output of this analysis can highlight the fact that maybe just a couple of the principal components can explain a good proportion of the variability in the data and therefore reduce the number of input columns to just those principal components. Regression is a type of predictive statistical model that belongs to the supervised learning family (James, Gareth, et al (2013)). Amongst all the regression models, linear regression is very attractive because it is easier to use, simple to interpret, and provides the user with many indicators that help assess the validity of the model. Linear regression allows to explain a dependent variable (Stain Damage in the present case) based on variation in one or multiple independent variables based on a linear relationship. It is advised to try and use linear regression first and investigate using nonlinear methods like regression trees or neural networks only if necessary. Nonlinear methods can fit a wide range of curves, but it generally requires more effort to implement. In addition, some types of models are difficult to understand, while others lack the statistical interpretations that accompany linear models under correct assumptions. 2.5. Predictive statistical model Now that some data was gathered, a predictive statistical model can be developed.

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