AESim: A Data-Driven Aircraft Engine Simulator

1 Introduction

Amidst current technological breakthroughs, numerous industries progressively adopt digital twins to build digital representations of their real-world systems. Digital twins are detailed replications of the physical world within interconnected digital models. They assist industries in refining decision-making, enhancing health monitoring, optimizing process design, and strengthening quality control, among other areas [Thelen et al., 2022; Errandonea et al., 2020].

The analysis and simulation of aircraft engine behavior have garnered significant attention in the aeronautical industry [Wang et al., 2017; Kim et al., 2020], primarily due to its performance, maintenance, safety, and sustainability implications. In the context of aircraft engines, sensors equipped within the engines capture so-called Continuous Engine Operational Data (CEOD) [Forest et al., 2018], which are multivariate time series (MTS) over entire flights. These measurements are vital for Prognostics and Health Management (PHM) applications [Coussirou et al., 2022; Lacaille and Langhendries, 2022; Forest et al., 2020]. However, missing data may occur due to sensor or data transfer failures or delays, leading to incomplete or biased information. Furthermore, it is challenging for aerospace companies to collaborate with academic partners from university laboratories to exploit this data in research projects, as it remains the property of airlines and is subject to contractual obligations, preventing them from being exchanged. Academic research requires opening the data for method validation and reproducibility. At Safran Aircraft Engines, we demonstrated the effectiveness of leveraging CEOD collected from the engines after each flight to build a representative model of the engine using conditional generative models. Subject to flight conditions and control settings, this digital twin tool makes it possible to simulate the engine's behavior if it had carried out the simulated flight mission. It makes it possible to provide CEOD of realistic simulated flights as performed by actual engines.

In this demonstration, we present AESim, an Aircraft Engine Simulator capable of reproducing the behavior of a real aircraft engine by replicating the complex engine dynamics. It addresses the challenges of missing data and industrial confidentiality constraints by generating realistic, simulated engine data for hypothetical missions. This capability enables the comparison of various engine behaviors under identical conditions. It provides valuable datasets for in-house and academic research, sidestepping confidentiality concerns and allowing for the development of robust PHM methods without relying on sensitive real-world data. AESim is based on a novel framework implementing our new architecture for Multivariate Time Series Conditional Generative Adversarial Nets (MTSCGAN) [Madane et al., 2023; Madane and Lacaille, 2023; Mirza and Osindero, 2014] and extending it to simulate the behavior of aircraft engines.

2 Case Study

The simulator is trained on continuous engine data recorded by aircraft engines belonging to the same fleet. Onboard sensors collect multiple measurements at different frequencies. We process them at a uniform frequency of 1 Hz. Throughout this demo, we present the generation of three parameters: Low-pressure rotor speed (N1), temperature at the entry of the combustion chamber (T) and Exhaust Gas Temperature (EGT), based on five external condition parameters, as shown in Figure 1, representing the simulated flight mission profile which are the ambient temperature, altitude, Mach number, Throttle Lever Angle and a boolean variable (not represented on the figure) indicating whether the engine is running or not.

3 SystemFramework

3.1 Methodology

We present an overview of our simulator framework in Figure 1, where a mission profile is used as input and the generated CEOD parameters represent the output. The workflow involves several steps:

Standardization of the input. The rawmultivariate time series data are normalized by subtracting the mean and dividing by the standard deviation of each feature to ensure equal contribution to the analysis.

Temporal Phase Partitioning. Continuous Engine Data can be extremely long, have variable lengths, and have different phases, resulting in different engine operational states. Multivariate time series are divided into distinct phases reflective of the multiple temporal dynamics within each flight (before, during, after Cruise). This partitioning facilitates the isolation of periods that exhibit homogeneous characteristics, enabling more targeted modeling in subsequent steps.

Segmentation within Phases. Each identified phase is further divided into fixed-duration segments, with each segment spanning 300 seconds and with a 20-timesteps overlap between consecutive segments. This segmentation strategy facilitates processing time series data with variable lengths, including extremely long flights, by eliminating restrictions on the input shape. By dividing the data into manageable segments, the approach ensures that the simulator can accommodate sequences of any length without pre-specifying a fixed input dimension. This flexibility is crucial since flight data have diverse temporal scales, and their length cannot be predetermined. The selection of segment length was informed by expert recommendations, reflecting a careful consideration of the engine's response to local physical phenomena, which typically is, at most, a five-minute duration. Additionally, this decision was guided by a balance between the retention of sufficient information to enable effective data generation and the computational feasibility, particularly due to the quadratic complexity of self-attention mechanisms with respect to the sequence length, making it computationally expensive for long sequences. This approach ensures that each segment is optimally sized to capture relevant dynamics without imposing undue computational demands, thereby maintaining the integrity of the generation process while accommodating the practical constraints of data processing.

Phase-wise and Segment-wise Data Generation. Data generation is performed using phase-specific models for each phase and corresponding segments. These models are designed to generate multivariate time series that mimic the real engine's statistical characteristics and temporal behavior as a response to the mission profile events-more details about the architecture of the generative models are in the following section. The conditional aspect of the generation is a critical component of our methodology. Each window was not generated separately; instead, the generation of a given window considered the previously generated window. This approach ensured continuity and coherence in the generated data, preserving the temporal dependencies.

De-normalization of the Generated Data. Re-applying the original mean and standard deviation values to the generated data, effectively returning it to its original scale.

Concatenation of Sequentially Generated Segments. The final step involves concatenating all sequentially generated segments to form a complete multivariate time series where each variable represents a CEOD parameter.

3.2 MTS-CGANArchitecture

This model generates context-dependent multivariate time series data by incorporating a conditional layer into its generation mechanism. It employs a generator, denoted as G (refer to Figure 2a), alongside a discriminator, D (see Figure 2b) for the training. The enhanced MTS-CGAN framework introduces conditioning not only based on the given context but also leverages the segment generated immediately prior. Here, the context refers to the mission profile, represented as a multivariate time series. As detailed in Section 3.1, the generation process for any specific window considers the window produced beforehand. This approach guarantees a seamless transition between consecutive data segments, effectively maintaining the temporal correlations inherent in the original multivariate time series.

The conditional generator (G) consists of two distinct components: The first component encodes the context of the simulated flight. This requires two inputs: a noise vector of dimension dz and the encoded context of dimension dy. The noise vector is encoded into a latent dimension space dy, then concatenated across the dimension known as 'channels.' This latent space's dimension is a data-dependent hyperparameter. We then apply linear transformations to the concatenated vectors to obtain a vector with a size equal to the target sequence length and dc channels, where dc must be tuned. Finally, we use a positional embedding vector to encode each element's position. It helps capture the sequence's order. Multiple consecutive blocks of the context encoder then process the final vector. The context encoder mirrors a conventional transformer encoder [Vaswani et al., 2017] where the multi-head self-attention layer extracts contextual inter-dependencies between the generated signal and the provided context. The second component of the conditional generator refines the generation process to incorporate information from the previously generated window. It takes the previous window as input and generates positional-aware embeddings from it. These embeddings are then channeled into the Adjustment Encoder. This encoder consists of two main layers. First, a multi-head self-attention layer processes the embeddings to extract features from the previously generated window. Then, a separate multi-head attention layer is used, with the query derived from the output of the self-attention layer, while the key and value are derived from the output of the generator's first component. This combination allows the generation process to incorporate the context and ensure continuity in the generated sequence. We note that the Adjustment Encoder block is iteratively repeated N times, where N is a tunable hyperparameter that should be adjusted according to the specific requirements of the generation task. The final output is processed by a convolutional layer with a kernel size of (1,1), where the number of output channels equals the target dimension.

The conditional discriminator (D) is designed to distinguish between real and generated multivariate time series data. It processes either real or generated CEOD inputs, each accompanied by the mission profile. Initially, it concatenates the CEOD and the profile mission multivariate time series along the channel dimension, followed by a linear transformation to produce an embedding. This embedding is then segmented into multiple patches, each with its positional encoding. These segmented patches are then input into the consecutive layers of the Transformer's encoder. A binary classifier leverages the final embedding to assess the likelihood of the input being real or generated, assigning a score to indicate this distinction. The architecture of this mechanism is illustrated in Figure 2b.

We use the Least Squares GAN (LSGAN) loss [Mao et al., 2017], replacing the standard GAN's [Goodfellow et al., 2020] cross-entropy loss with a least squares loss for better training stability and convergence. An extra loss term is added to the generator to ensure seamless transitions in flight sequences by aligning overlapping segments of 20 data points each, preserving sequence continuity without data repetition. Both discriminator and generator parameters are optimized to minimize their respective loss functions, LD and LG.

4 Conclusion

In this demo, we introduced AESim, a novel aircraft engine simulator framework using a Transformer-based architecture to model multivariate time series in conditional generation tasks. The model learned the distribution of observed data for each context simultaneously. Self-attention mechanisms effectively captured the conditional generation aspect, maintaining the complex dynamics of the engine parameters. Although in this demonstration, we have focused on a single complex aircraft engine use case, it is interesting to note that the approach can be extended to other industrial use cases. The system is being tested internally at Safran's DataLab and there are plans to test it in other company departments.