# Residual Life Prediction of Gas-Engine Turbine Blades Based on Damage Surrogate-Assisted Modeling
## 2 Methods
### Surrogate-Model Construction
To form the dependence of the damage on the engine parameters, surrogate modeling can be used, the purpose of which is to build an approximation model to predict the values of the output parameters on the basis of the input parameters from the range of permissible values. **Step 5:** The surrogate model of the blade is a nonlinear-regression model that is constructed using a combination of ensemble machine-learning methods such as model stacking and boosting. The main steps to construct the proposed surrogate model (Figure 6) were:  
1. Data normalization: Each variable was individually scaled, such that it was in the given range between 0 and 1. The transformation was calculated as follows: \[X_{norm}=\frac{X-X_{min}}{X_{max}-X_{min}}\] (7)
2. Regime split and sampling: Since the original target distribution was biased towards near-zero values, which is explained by damage accumulation under usual working conditions, regime split was performed. The data points were split into two groups: working and extreme conditions. Then, the input dataset for the model was obtained by uniform sampling from these two distributions using the bootstrapping technique (random sampling with replacement) to compensate for imbalance between the regimes. 3. Validation scheme: The resampled dataset from the previous step was divided into training and test sets with partitioning ratios of 80% and 20%, respectively. The training set was then randomly divided into ten subsets in order to perform \(k\)-fold cross-validation (CV) during model training. 4. Model training: Each so-called \"weak\" submodel included in the ensemble was first trained on (\(k-1\)) folds of the training data, while the remaining fold was used to make predictions, as well as an evaluation set for early stopping to prevent the submodel from overfitting. The following procedure was repeated \(k\) times for each fold. Further, this submodel was fitted on the whole training set, and predictions were then made on the test set. The submodel's predictions from the training set were then used as features to build the master (stacked) model, which in turn was used to make final target predictions on the test set. For each of the models, the root-mean-square error (RMSE) was chosen as an objective function, as well as an accuracy metric during validation. 5. Model selection: Hyperparameters such as learning rate, maximal tree depth, and number of leaves were optimized for each model using randomized search with independent threefold cross-validation, which showed relatively better performance than that of grid search in finding a global minimum [17]. Code availability: The source code, pretrained ensemble submodels, and full surrogate model were deposited in a GitHub repository ([[https://github.com/raevskymichail/ciam_ml_model](https://github.com/raevskymichail/ciam_ml_model)]([https://github.com/raevskymichail/ciam_ml_model](https://github.com/raevskymichail/ciam_ml_model))) [18]. The advantages of the proposed approach are:  
1. Several critical zones are tracked. 2. The life counter can be adapted to a specific part or GTE. 3. Results of 3D calculations with consideration of plasticity, creep, and material anisotropy can be used. 4. Loading history can be considered. 5. It is possible to account for various damage modes and residual stress in parts. 6. The surrogate model is part of a comprehensive diagnostic solution.