# Residual Life Prediction of Gas-Engine Turbine Blades Based on Damage Surrogate-Assisted Modeling

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## Abstract

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## 1. Introduction

- Methods based on the use of equations obtained using simplified models; for example, the simple relation between rotor speed and part stress state can be used.
- Methods based on big-data analysis and the formation of correlation dependencies between measured parameters and failures [6].
- Methods based on nondestructive and destructive testing (service-based approach). In this method, it is necessary to find correlation between microstructural degradation and temperature exposure time, and/or service duration [7].

- The deterioration of engine parameters during operation, and the fact that individual characteristics of both parts and engines are not considered.
- Damage assessment is usually performed for only one critical zone; however, during operation, the critical zone may change.
- Numerical models are usually oversimplified and do not consider the plasticity, creep (stress redistribution), and anisotropy of material characteristics.
- As calculations are performed on the most unfavorable design point, and a substantial safety factor is used to ensure failure-free operation, this causes many components to be discarded too early.

## 2. Methods

#### 2.1. GTE Model

#### 2.2. Damage Prediction

^{®}software.

#### 2.3. Surrogate-Model Construction

- Selection of parameters and their range that determine the stress state of the blade.
- Determination of material blade characteristics.
- Construction of solid-state and finite-element (FE) models of the blade.
- Calculation of strength with consideration of material anisotropy and nonlinearities.
- Formation of blade surrogate model.

**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.

**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

^{®}software was used to generate mesh and perform calculations (see Appendix B).

**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).

**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:

- 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:$${X}_{norm}=\frac{X-{X}_{min}}{{X}_{max}-{X}_{min}}$$
- 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.
- 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.
- 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.
- 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].

- Several critical zones are tracked.
- The life counter can be adapted to a specific part or GTE.
- Results of 3D calculations with consideration of plasticity, creep, and material anisotropy can be used.
- Loading history can be considered.
- It is possible to account for various damage modes and residual stress in parts.
- The surrogate model is part of a comprehensive diagnostic solution.

## 3. Results and Discussion

- 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.
- A significant increase in damage during the summer period.
- 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.

## 4. Conclusions

## 5. Future Work

- shutdowns, including emergencies;
- transient modes;
- scatter in blade dimensions;
- the influence of creep and fatigue on each other;
- fuel and air quality;
- contamination of the turbine gas path.

- computational studies of heat-stress state of the unit in transient modes;
- increasing the complexity of the used mathematical gas-engine models;
- improving the material models; and
- Correction factors to consider the acceleration of the damage-accumulation process.

## 6. Grant Information

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

COT | Compressor outlet temperature |

FEM | Finite-element model |

GTE | Gas-turbine engine |

HPT | High-pressure turbine |

LCF | Low-cycle fatigue |

LDA | Linear damage accumulation |

LMP | Larson–Miller parameter |

RPM | Revolutions per minute |

## Appendix A. Terminology

## Appendix B. Information about FE Models

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**Figure 1.**Proposed methodology for surrogate model: usage scenario of surrogate model in real operation conditions. ${T}_{atm}$, atmospheric air temperature; ${H}_{atm}$, atmospheric air humidity; ${Q}_{fuel}$, fuel consumption; ${t}_{work}$, regime duration; ${W}_{GTE}$, gas-turbine-engine power; $COT$, compressor-outlet temperature; $TIT$, turbine-inlet temperature; ${D}_{zone}$, separately estimated damage for each critical zone.

**Figure 2.**Proposed gas-turbine-engine (GTE) model. LPC, low-pressure compressor; HPC, high-pressure compressor; LPT, low-pressure turbine; HPT, high-pressure turbine; Cp volume, chamber with constant volume.

**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 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.

**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.

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**MDPI and ACS Style**

Vasilyev, B.; Nikolaev, S.; Raevskiy, M.; Belov, S.; Uzhinsky, I.
Residual Life Prediction of Gas-Engine Turbine Blades Based on Damage Surrogate-Assisted Modeling. *Appl. Sci.* **2020**, *10*, 8541.
https://doi.org/10.3390/app10238541

**AMA Style**

Vasilyev B, Nikolaev S, Raevskiy M, Belov S, Uzhinsky I.
Residual Life Prediction of Gas-Engine Turbine Blades Based on Damage Surrogate-Assisted Modeling. *Applied Sciences*. 2020; 10(23):8541.
https://doi.org/10.3390/app10238541

**Chicago/Turabian Style**

Vasilyev, Boris, Sergei Nikolaev, Mikhail Raevskiy, Sergei Belov, and Ighor Uzhinsky.
2020. "Residual Life Prediction of Gas-Engine Turbine Blades Based on Damage Surrogate-Assisted Modeling" *Applied Sciences* 10, no. 23: 8541.
https://doi.org/10.3390/app10238541