# Residual Life Prediction of Gas-Engine Turbine Blades Based on Damage Surrogate-Assisted Modeling
## 2 Methods
### Surrogate-Model Construction  
To predict residual life, a machine-learning-assisted surrogate-modeling approach was proposed [1]. This approach is based on a series of 3D stress-state calculations. The obtained surrogate model, along with the GTE model (Figure 1) were used to evaluate the accumulated damage to the turbine blades in real time using the measured parameters. The proposed approach may also be used to determine the influence of operating conditions, such as air inlet parameters, on the engine parts' life. The method consists of the following steps:  
1. Selection of parameters and their range that determine the stress state of the blade. 2. Determination of material blade characteristics. 3. Construction of solid-state and finite-element (FE) models of the blade. 4. Calculation of strength with consideration of material anisotropy and nonlinearities. 5. Formation of blade surrogate model. These steps are described in detail below, some information about the machine learning terms is given in Appendix A. **Step 1:** The choice of parameters determining the stress state of the blade is based on the GTE model (Figure 1). For high-pressure turbines (\(HPT\)), such parameters are turbine inlet temperature (\(TIT\)), RPM, and compressor outlet temperature (\(COT\)). The range of assigned parameters is based on operation history (including engine prototypes) or on the results of the use of thermodynamic models of the engine. Figure 3: Typical relaxation curve. **Step 2:** Experimental determination of material blade characteristics. The test regimes depend on the type of material; for example, for single-crystal blades, it is necessary to test specimens with various crystallographic orientations [14]. After the experiments, it is necessary to form a set of structural strength characteristics of the material [14]. At this stage, the damage-accumulation rule should also be checked. **Step 3:** After constructing a solid model of the blade, the FE model is generated (Figure 4) using second-order hexagonal elements consisting of 454,180 nodes and 138,542 elements. ANSYS(r) software was used to generate mesh and perform calculations (see Appendix B). After constructing a solid model of the blade, the FE model is generated (Figure 4). It is recommended to use the second-order elements and check the quality of the FE model. **Step 4:** At this stage, the blades' stress-strain state is calculated considering plasticity, creep, and geometric nonlinearity. Depending on the statement of the problem, the contact interaction between blade and disk, and the anisotropy of the material blade characteristics can be considered. For single-crystal turbine blades, the anisotropy of the material characteristics must be considered. For this purpose, a material model is formed with the properties determined by a preliminary study for various crystallographic directions [14]. First, at this stage, preliminary calculations of the blades' strength in several regimes are performed. Using the results of these calculations, the critical locations of the turbine blades are determined (Figure 5). For _HPT_ blades, the complexity of the task (and execution time) can be reduced by using the assumption of maintaining the cooling effectiveness (\(\Theta\)) when changing the cycle parameters. If the blade's temperature (\(T_{m}\)) and the parameters of the cycle on any mode \(i\) are known, in each of the nodes of the FE model, the cooling effectiveness parameter (\(\Theta\)) can be calculated as follows:  
\[\Theta=\frac{TIT-T_{m}}{TIT-COT} \tag{6}\]  
where \(TIT\) is the turbine-inlet temperature, \(T_{m}\) is the metal temperature, and \(COT\) is the compressor-outlet temperature. Calculation of the accumulated damage must take place in real  
Figure 4: Finite-element (FE) model of the considered blade. Figure 5: Critical zones (1–8) of considered blade. time; this can be achieved by different methods, including surrogate modeling [15; 16].