**1. Introduction**

In the past twenty years, high-speed railway systems are gradually becoming one of the most popular transportation services because of their significant advantages in speed and energy efficiency [1–3]. The running gears are critical parts to ensure the safety of high-speed train operations. To precisely detect the real-time health status of running gears is very challengeable. In reality, sensor signals of running gears in high-speed trains have a very high degree of complexity, for instance, messy signals from bogie, bearing temperature, gear temperature, working environments and random noises. Moreover, there are only small-scale historical failure data available among large volumes of monitoring data streams. Incomplete training resources might easily raise detection errors.

With the rapid development of train sensor technology, data-driven FD methods have been well studied in the last century. Many multivariate statistical methods have been widely applied in the fault detection fields [4–6], for example, principal component analysis (PCA), partial least squares (PLS) and CCA. PCA was one of the earliest dimensionality reduction methods to process high-dimension signal data for FD purposes [7,8]. PCA projects high-dimension input data into low-rank subspaces while retaining the main information of the original data within a few top latent dimensions. Moreover, PCA FD models are derived from a large scale of normal status signals and generate fault alarm thresholds for incoming error signals. PLS and CCA are widely utilized to develop advanced FD models [6,9,10]. PLS decomposes the covariance matrices of two sets of variables into relational subspaces and residual subspaces. Then, the regression analysis to covariance structure estimates the multi-direction of one set of variables that explains the maximum multidimensional variance direction of another set of variables. CCA identifies linear

**Citation:** Zheng, H.; Zhu, K.; Cheng, C.; Fu, Z. Fault Detection for High-Speed Trains Using CCA and Just-in-Time Learning. *Machines* **2022**, *10*, 526. https://doi.org/10.3390/ machines10070526

Academic Editor: Yaguo Lei

Received: 19 May 2022 Accepted: 20 June 2022 Published: 28 June 2022

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combinations between two groups of variables to maximize the overall group correlation. Multi-set CCA resolved feature fusion of multiple groups of variables [11].

Chen and Ding [12] designed a general CCA-based FD infrastructure for non-Gaussian processes which aimed to boost the fault detection rate (FDR) under an acceptable false alarm rate (FAR). Peng and Ding [13] have proposed CCA-based distributed monitoring processes within partly-connected networks, which reduced communication costs and risks and avoided a significant drop in system performance. Chen and Chen [6] introduced a single-side CCA (SsCCA) model with promising FD performance using single-side neural networks. Chen and Li [14] had proposed a stacked approach, so called neural networkaided canonical variate analysis (SNNCVA), which showed satisfactory FD performance for nonlinear datasets. Garramiola and Poza [15] introduced a data-driven approach of fault diagnosis to build hybrid fusion models to detect, isolate and classify sensor faults. Kou and Qin [16] extended fault diagnosis methodology into tensor space to deal with multisensor data with high precision and convergence speed. Zhao and Yan [17] provided a comprehensive review which summarized state-of-the-art deep learning (DL) technologies applied on machine health monitoring (MHM). Niu and Xiong [18] proposed a novel fault Petri net fault detection and diagnosis (FDD) model to analyze signals of speed sensors of high-speed trains. Fu and Huang [19] proposed a fault diagnosis method based on the longshort-term memory (LSTM) recursive neural network (RNN) to reduce the steps of signal preprocessing and optimize prediction accuracy. Cheng and Guo [20] designed a real-time prediction framework for running state of running station based on multi-layer BRB and priority scheduling strategy. Guan and Huang [21] created a particle swarm optimization algorithm based on wavelet variation and a least squares support vector machine to avoid falling into local extremum problems. Sayyad and Kumar [22] introduced a survey to review service life prediction technologies of real-time health monitors of cutting tools from perspectives of modeling, systems, data sets and research trends. Capriglione and Carratu [23] proposed an FD method using a nonlinear autoregressive with Exogenous Inputs (NARX) neural network as a residual generator for online FD of travel sensors. Shabanian and Montazeri [24] proposed an online FD and diagnosis algorithm based on the neural fuzzy, and adaptive analytic method and neural network to track faults online.

JITL technologies involve collecting the most relevant samples as training data for online query and making predictions of local modeling running time [25–27]. Compared with similar samples in historical databases, the signal status of online query could be possibly acquired in real time. Robust JITL strategies to leverage the weights of high leakage points of signals such as outliers had been successfully applied to the FD tasks [28]. A simulation study showed that the combined JITL-PCA models outperformed PCA in the analyzing of nonlinear signals [26]. In addition, neural network methods and the stochastic hidden Markov model (HMM) were studied to improve FD performance of dynamic systems [29,30].

Motivated by the previous studies, we designed a novel CCA-JITL model to analyze real-time signals from running gears of high-speed trains. The model was built and testified using real-world datasets. The algorithm split the data input into two groups and verified the system performance by group comparison The evaluation demonstrated that the accuracy of FD detection was significantly improved. The algorithm detects the data in groups and verifies the two groups of results, and the proposed system infrastructure was also applicable to enhance PCA and PLS FD models.

The rest of this article is content as follows. Section 2 gives introduction the structure of running gears system, experiment design and datasets. Section 3 presents theoretical foundations of the proposed method. Section 4 presents evaluation results of a FD use case and discussion of the results. Finally, Section 5 summarizes this paper study.
