Neural Network for the Statistical Process Control of HVAC Systems in Passenger Rail Vehicles

Abstract

In the rail industry, coach temperature regulation has become a crucial task to improve passenger thermal comfort. Over the past few years, European standards have required rail operators to implement monitoring systems for the control of heating, ventilation and air conditioning (HVAC) of passenger rail vehicles. These systems, based on modern automated sensing technologies, have created new data-rich scenarios and call for new methods to deal with high-dimensional, high-correlated and heterogeneous data. In this article, an autoencoder, which is a particular type of neural network developed to model unlabelled data and automatically extract significant features, is utilised to develop a nonparametric process monitoring approach. Two control charts based on statistics $H^2$ and SPE are built in the feature space and the residual space, respectively. Through operational HVAC data collected on board passenger vehicles, the proposed approach is shown to be capable of simultaneously monitoring and detecting anomalies that may have occurred in the data streams acquired from each train coach, even though it is not limited to the application hereby investigated. Additionally, via a numerical investigation, the Phase II fault detection performance is compared with that of a simpler linear dimension reduction method and two more complex NN architectures.

Appendix

In this Appendix, the Phase II fault detection performance of the proposed method is compared with that of PCA, AE with more than one hidden layer, referred to as DeepAE, and Variational AE, referred to as VAE [6, 11]. The PCA is regarded as a simpler linear dimension reduction method and is used as the benchmark to prove the effectiveness of non-linear approaches. Whereas DeepAE and VAE are regarded as alternative to the proposed NN with more a complex architecture.

Note that, to allow for a fair comparison, the proposed AE, the DeepAE and the VAE must be chosen with a number of code layer nodes equal to the number of components retained in the PCA. In this regard, we compare the performance of the proposed AE with that of the competing methods by setting the code layer dimension hyperparameter equal to 2 and 12. The former turned out indeed to be the optimal number of extracted features by PCA, as they explained the $82\%$ of the total variance [16]. Whereas, the latter is the optimal choice for the number of code layer nodes for the proposed AE, as already reported in Table 2. Also in this case, as stated in Sect. 2.3 for the proposed AE, the $H^2$ and SPE statistics and the relative UCLs for all competing methods are estimated by means of the block bootstrap with $\alpha = 0.05$. The Phase II fault detection performance is explored by means of a numerical investigation based on four different Phase II scenarios. The latter is based on data generated by resampling and transforming $N_s = 10000$ observations from the training set in order to simulate Phase II non-normal operating conditions with the following severity levels:

• 1. the means of the variables $T_\text {Return}$ and $T_\text {Supply}$ of one coach, say coach # 1, are shifted by an amount $\Delta$ equal to two units of the relative standard deviation, i.e., $\Delta = 2\sigma$ (Scenario 1);

• 2. the means of the variables $T_\text {Return}$ and $T_\text {Supply}$ of one coach are shifted by $\Delta = 3\sigma$ (Scenario 2);

• 3. the means of the variables $T_\text {Return}$ and $T_\text {Supply}$ of two coaches, say coach # 1 and # 2, are shifted by $\Delta = 2\sigma$ (Scenario 3);

• 4. the means of the variables $T_\text {Return}$ and $T_\text {Supply}$ of two coaches are shifted by $\Delta = 3\sigma$ (Scenario 4).

Trivially, if either the $H^2$ or SPE statistics exceeds the value of the corresponding UCL, the fault is counted as successfully detected, otherwise, no alarm is signalled. Then, the Phase II performance is measured through the FDR index, calculated as $\text {FDR = TN}/N_s \times 100 \%$, where TN is the number of fault samples correctly identified. FDRs of the four competing methods are reported in Tables 3 and 4 for a number of code layer nodes equal to 2 and 12, respectively.

Table 3 FDR (%) for a code layer dimension hyperparameter equal to 2 in the four scenarios described in Sect. 2.3. The best performance is highlighted in bold

Table 4 FDR (%) for a code layer dimension hyperparameter equal to 12 in the four scenarios described in Sect. 2.3. The best performance is highlighted in bold

In particular, Table 3 demonstrates that, even when we choose the best latent representation for the PCA, the latter is outperformed by the proposed method, which in fact performs better also than DeepAE and VAE, in all considered scenarios.

From Table 4, when the code layer dimension is set equal to 12, the Phase II performance of the proposed AE, although outperforming the PCA in all scenarios, is instead outperformed by VAE in Scenario 2 and DeepAE in Scenario 3 and 4. This indicates that the proposed AE is still the best in detecting small deviations from normal behaviours with respect to more complex NN architectures. It is however clear that in all cases PCA underperforms all competing non-linear approaches.