Intelligent Method of Identifying the Nonlinear Dynamic Model for Helicopter Turboshaft Engines

Abstract

This research focused on the helicopter turboshaft engine dynamic model, identifying task solving in unsteady and transient modes (engine starting and acceleration) based on sensor data. It is known that about 85% of helicopter turboshaft engines operate in steady-state modes, while only around 15% operate in unsteady and transient modes. Therefore, developing dynamic multi-mode models that account for engine behavior during these modes is a critical scientific and practical task. The dynamic model for starting and acceleration modes has been further developed using on-board parameters recorded by sensors (gas-generator rotor r.p.m., free turbine rotor speed, gas temperature in front of the compressor turbine, fuel consumption) to achieve a 99.88% accuracy in identifying the dynamics of these parameters. An improved Elman recurrent neural network with dynamic stack memory was introduced, enhancing the robustness and increasing the performance by 2.7 times compared to traditional Elman networks. A theorem was proposed and proven, demonstrating that the total execution time for N Push and Pop operations in the dynamic stack memory does not exceed a certain value O(N). The training algorithm for the Elman network was improved using time delay considerations and Butterworth filter preprocessing, reducing the loss function from 2.5 to 0.12% over 120 epochs. The gradient diagram showed a decrease over time, indicating the model's approach to the minimum loss function, with optimal settings ensuring the stable training.

Keywords: Elman recurrent neural network with dynamic stack memory; accuracy; dynamic model; engine starting and acceleration; helicopter turboshaft engines; identifying; sensors; training.

Figure 1

Diagrams of changes in the helicopter turboshaft engine parameters (using for example, the TV3-117 engine) at starting mode: (a) fuel consumption, (b) gas-generator rotor r.p.m., (c) free turbine rotor speed, (d) gas temperature in front of the compressor turbine (author’s research).

Figure 2

Diagram of changes in the helicopter turboshaft engine’s (using for example, the TV3-117 engine) gas temperature in front of the compressor turbine after applying the low-frequency filtering procedure at starting mode (author’s research).

Figure 3

The dependency diagrams of the helicopter turboshaft engine parameters: (a) fuel consumption, (b) gas-generator rotor r.p.m. (author’s research).

Figure 4

The statistical characteristics of the helicopter turboshaft engine parameters (author’s research).

Figure 5

Implementation diagram of a memory layer for a modified Elman neural network with dynamic stack memory ([76], p. 134, URL: https://swsys.ru/index.php?page=article&id=3910&lang=.docs (accessed on 28 June 2024)).

Figure 6

Modified Elman neural network with dynamic stack memory as a helicopter TE dynamic model (author’s research).

Figure 7

The TV3-117 turboshaft engine parameters’ dynamics time series using digitized oscillograms. (Black curve) Gas-generator rotor r.p.m; (Blue curve) free turbine rotor speed; (Orange curve) gas temperature in front of the compressor turbine (author’s research).

Figure 8

Cluster analysis results: (a) training set, (b) test set (author’s research).

Figure 9

Diagram of the helicopter turboshaft engines parameters (using the TV3-117 engine as an example) after the low-frequency filtering procedure with an eighth-order Butterworth filter: (a): gas-generator rotor r.p.m; (b) free turbine rotor speed; (c) gas temperature in front of the compressor turbine (author’s research).

Figure 10

Diagrams of the spectral characteristics of the helicopter turboshaft engine parameters (using the TV3-117 engine as an example): (a) gas-generator rotor r.p.m., (b) free turbine rotor speed, (c) gas temperature in front of the compressor turbine (author’s research).

Figure 11

Scheme of the training sample loading of the helicopter turboshaft engine’s thermogas-dynamic parameters and the processing of experimental data by the proposed algorithm (author’s research).

Figure 12

Diagrams of the transient processes of the helicopter turboshaft engine parameters at starting mode (using the TV3-117 engine as an example): (a) gas-generator rotor r.p.m., (b) free turbine rotor speed, (c) gas temperature in front of the compressor turbine (author’s research).

Figure 13

Diagrams of the difference between the simulated and experimental processes of the helicopter turboshaft engine at starting mode (using the TV3-117 engine as an example): (a) gas-generator rotor r.p.m., (b) free turbine rotor speed, (c) gas temperature in front of the compressor turbine (author’s research).

Figure 14

Diagrams of the transient processes of the helicopter turboshaft engine parameters at acceleration mode (using the TV3-117 engine as an example): (a) gas-generator rotor r.p.m., (b) free turbine rotor speed, (c) gas temperature in front of the compressor turbine (author’s research).

Figure 15

Diagrams of the difference between the simulated and experimental processes of the helicopter turboshaft engine at acceleration mode (using the TV3-117 engine as an example): (a) gas-generator rotor r.p.m., (b) free turbine rotor speed, (c) gas temperature in front of the compressor turbine (author’s research).

Figure 16

Diagram of the influence of epoch number passed the mean square error (author’s research).

Figure 17

Diagram of accuracy metric (author’s research).

Figure 18

Diagram of loss function (author’s research).

Figure 19

Diagram of changes in loss function gradients (author’s research).

Figure 20

Diagrams of the distribution surfaces U₁(k) (a), U₂(k) (b), and U₃(k) (c) (author’s research).

Figure 21

The resulting k-fold cross-validation diagrams (author’s research).

Figure 22

The AUC-ROC curves. (a) Proposed modified Elman neural network with dynamic stack memory; (b) traditional Elman neural network developed in [34,66]; (c) cubic spline interpolation (author’s research).