Fault diagnosis of aero-engines using transfer dispersion entropy and dispersion patterns

RESEARCH ARTICLE Fault diagnosis of aero-engines using transfer dispersion entropy and dispersion patterns Hong Zhang1, Yin Zhang2, Jingna Liu2, Keqiang Dong * 2 1 Basic Courses Department, Tianjin Sino-German University of Applied Sciences, Tianjin, China, 2 College of Science, Civil Aviation University of China, Tianjin, China * Abstract OPEN ACCESS Citation: Zhang H, Zhang Y, Liu J, Dong K (2026) Fault diagnosis of aero-engines using transfer dispersion entropy and dispersion patterns. PLoS One 21(5): e0348356. https:// doi.org/10.1371/journal.pone.0348356 Editor: Haris Calgan, Balikesir Universitesi, TÜRKIYE Received: November 18, 2025 Accepted: April 15, 2026 Dispersion entropy (DE) can effectively detect the chaotic features in ordered sequences. However, DE is only defined by the probability distribution of static dispersion patterns, ignoring the dynamic transitions between pairwise dispersion patterns. Therefore, in this paper, by introducing the transition probability between pairwise dispersion patterns, we propose the transfer dispersion entropy (TDE) to detect the chaotic characteristics of the system. Additionally, based on both the difference in the number of each dispersion patterns and the difference in the transfer probability matrix, we define a dissimilarity measure for different sequences, namely transfer dissimilarity based on dispersion patterns (TDDP). Then, the proposed methods are verified on numerical simulation data and NASA-CMAPSS aero-engine simulation data.Compared with the existing entropy algorithms, the results show that TDE can not only capture more detailed chaotic changes, but also identify the early degradation of gas path components by detecting abnormal shifts in pattern transition behaviors, enabling more timely fault warnings.Finally, the combination of TDDP and multidimensional scaling can be used for similarity classification of aero-engine simulation time series. Published: May 27, 2026 Copyright: © 2026 Zhang et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data availability statement: The engine data are available from https://data.nasa.gov/dataset/ cmapss-jet-engine-simulated-data. Funding: This work was supported by the Joint Funds of the Natural Science Foundation of Tianjin (No. 23JCZDJC00070 to Keqiang Dong) and the The Key Laboratory of Civil Introduction When mechanical failures occur in equipment such as gearboxes and aircraft engines, the collected data tend to exhibit more non-stationary, aperiodic, and nonlinear characteristics. Accurately identifying fault-related information from the obtained time series is essential for timely equipment maintenance. Currently, several advanced signal processing methods are employed in fault detection for large-scale machinery due to their ability to effectively analyze dynamic information within time series. For instance, Huo et al. [1] applied wavelet transform to decompose vibration signals into multiple layers and then utilized a particle swarm optimization algorithm to determine the optimal parameters of a pulse-based model, achieving promising fault diagnosis results. Liu et al. [2] demonstrated how time¨Cfrequency domain PLOS One | https://doi.org/10.1371/journal.pone.0348356 May 27, 2026 1 / 23 Aircraft Airworthiness Technology Foundation (SH2020112701 to Keqiang Dong). Competing interests: The authors have declared that no competing interests exist. analysis can be used for fault detection in tandem systems: variational mode decomposition was first applied to extract characteristic frequency bands from current signals, after which the Shannon entropy of these band signals was calculated to assess signal complexity. Mohsen and El-Yazeed [3] adopted an autoregressive moving average model to preprocess circuit responses under different fault conditions, deriving a set of features to train and test a backpropagation neural network for fault classification. However, these signal processing approaches often rely on empirical or prior knowledge [4] and are associated with high computational complexity. Moreover, they typically require the predefinition of numerous parameters that are difficult to select appropriately. Owing to their reliance on fewer parameters, independence from prior knowledge, and straightforward applicability without pretreatment, entropy-based approaches have been widely adopted in fault diagnosis [5]. In their work [6], Huo et al. provide a thorough review of the theoretical development of several foundational entropy methods, clarifying their interrelations. They further outline representative applications of entropy in mechanical fault detection. As a measure of system complexity, approximate entropy (AE) [7] is utilized to quantify repetitive transients in machine condition monitoring [8]. The introduction of sample entropy (SE) [9], which assesses series complexity by computing the proportion of newly generated patterns, has led to a broader application of entropy theory in fault diagnosis [10,11]. Fuzzy entropy (FE) [12], as a modified version of SE, incorporates fuzzy theory to compute state probabilities, thereby achieving greater stability and demonstrating reliable performance in bearing fault classification [13]. Despite their utility as fault detection tools, these methods possess certain limitations. SE exhibits significant variability and lacks continuity [14]. Moreover, when processing long data series, both AE and FE suffer from lower computational efficiency [15]. To address these issues, Bandt and Pompe [16] proposed permutation entropy (PE), which evaluates dynamic complexity through ordinal permutation and offers a new perspective for mechanical fault detection [17]. Recognizing that PE does not account for amplitude differences, Rostaghi and Azami introduced dispersion entropy (DE) [18], an irregularity measure that incorporates amplitude relationships. DE is less sensitive to sudden signal changes and can effectively identify chaotic features within ordered sequences, making it applicable in fields such as simulation and diagnosis [19,20]. Meanwhile, nonlinear dynamic indicators such as Lempel-Ziv complexity (LZC) have been integrated with symbolic patterns. Li et al.have proposed two notable LZCbased indicators: the multivariate threshold-adjusted permutation LZC (MTPELZC) [21] to enhance sensitivity to permutation patterns in multivariate systems, and the multiscale similarity fuzzy LZC (MSFLZC) [22] to preserve correlation information between dispersion patterns. However, both methods have limitations: MTPELZC requires complex parameter selection for multivariate settings and suffers from high computational cost; MSFLZC is sensitive to similarity tolerance and also computationally expensive. More importantly, neither model (...truncated)