# Residual Life Prediction of Gas-Engine Turbine Blades Based on Damage Surrogate-Assisted Modeling
## 3 Results and Discussion  
Machine-learning-assisted surrogate modeling was successfully applied to a number of engineering problems [19; 20; 21; 22]. This encourages its use in optimization and inference methods suited for complex models. Such surrogates can mimic comprehensive physical models while remaining computationally inexpensive, which is often a prerequisite for many engineering applications where available computing resources and maintenance are limited.  
In that paper, the HPT rotor blade was considered. Figure 4 shows the FE model of the considered blade. Figure 7 shows the temperature field for one of the regimes.  
Furthermore, by varying parameters \(TIT\), \(COT\), and \(RPM\) for critical zones using the methods described above, surrogate models for different critical zones were constructed. The constructed surrogate models of the turbine blade, based on boosting and stacking ensemble machine-learning methods, showed satisfactory accuracy, which remained stable for both typical and extreme working conditions (Figure 8).  
Figure 6: Overview of machine-learning-based surrogate model.  
Figure 7: Blade-temperature field.  
To demonstrate the relevance of the approach, we simulated the operation of the considered GTE power plant in two Russian cities. For this purpose, information about the weather over the last five years was used [23]. Figure 9a shows the average temperature values for daily segments. Figure 9b shows a comparison of the accumulation of total damage in one of the critical zones (Zone 6 in Figure 5) of the considered blade. Analysis of the results showed the following:  
1. Significant impact of the place of operation. For the considered zone, the total damage value over five years was more than four times higher in the Krasnodar area compared to the Moscow area.
2. A significant increase in damage during the summer period.
3. An increase in the rate of damage accumulation from year to year. For example, the damage rate for 2017 was almost twice as high as that for 2015.  
We also considered how linear damage accumulation depends on sampling rate (Figure 10) relative to the damage accumulation obtained on 1 h resolution data using a relative-error (\(RE\)) formula:  
\[RE=\frac{D_{i}-D_{1h}}{D_{1h}}*100\% \tag{8}\]  
where \(D_{i}\) and \(D_{1h}\)are damage accumulation calculated on data with a given sampling rate and on 1 h resolution regime data, respectively.  
Result showed that, for the considered GTE data, averaging on a given time step up to 1 month, values had little impact on the resulting linear damage accumulation in comparison with damage accumulation calculated on regime data with a 1 h resolution (\(RE<0.12\%\) for 5 years of turbine operation).  
Figure 8: Validation results of surrogate model on hold-out test set: (**a**) true vs predicted plot for used submodels; (**b**) true vs predicted plot for master model; (**c**) true minus predicted plot for master model.  
Figure 10: Impact of sampling rate on linear damage accumulation. Relative error (RE) between damage accumulation calculated on 1 h data and averaged on a given period.  
Figure 9: Linear damage accumulation from surrogate model for blades working under different temperature conditions: (**a**) average month temperatures in Moscow and Krasnodar areas for 2015–2020 [23]; (**b**) linear damage accumulation in critical Zone 5 (5) over 5 year period of operation.