Industrial process monitoring is a critical application of multivariate time-series (MTS) anomaly detection, especially crucial for safety-critical systems such as nuclear power plants (NPPs). However, some current data-driven process monitoring approaches may not fully capitalize on the temporal-spatial correlations inherent in operational MTS data. Particularly, asynchronous time-lagged correlations may exist among variables in actual NPPs, which further complicates this challenge. In this work, a reconstruction-based MTS anomaly detection approach based on a temporal-spatial transformer is proposed. It employs a two-stage temporal-spatial attention mechanism combined with a multi-scale strategy to learn the dependencies within normal operational data at various scales, thereby facilitating the extraction of temporal-spatial correlations from asynchronous MTS. Experiments on simulated datasets and real NPP datasets demonstrate that the proposed model possesses stronger feature learning capabilities, as evidenced by its improved performance in signal reconstruction and anomaly detection for asynchronous MTS data. Moreover, the proposed TS-Trans model enables earlier detection of anomalous events, which holds significant importance for enhancing operational safety and reducing potential losses in NPPs.

As a key equipment of the reactor coolant system, the reactor coolant pump’s operational state can have a direct impact on the coolant circulation. However, the harsh working environment can accelerate the process of equipment deterioration for the reactor coolant pump while the current alarm mechanism cannot detect the deterioration of equipment performance at the early stage. This issue may lead to anomalies developing into faults and causing unplanned shutdowns and reactor trips. In this paper, we proposed a transformer‐based anomaly detection model for reactor coolant pump condition monitoring. On the basis of retaining the time‐dependent capture ability of the original transformer network for sequence data, the proposed model has obtained a stronger learning ability of the spatial correlation between variables through the application of the attention mechanism. Historical operating data under normal conditions are used for the training process and the reconstruction errors of input signals are utilized to identify anomalies. The experimental results have indicated that the proposed model possesses stronger feature learning capabilities, evidenced by improved performance in signal reconstruction and anomaly detection, which can help to detect the abnormal status at an earlier stage.

The tilt angle of sunspot groups plays a crucial role in solar dynamo models for the generation of the poloidal field, yet the statistical properties of the tilt angle are not fully comprehended. This study employs magnetograms from the Solar and Heliospheric Observatory/Michelson Doppler Imager and Solar Dynamics Observatory/Helioseismic and Magnetic Imager to measure the tilt angles of 11,373 sunspot groups over the period from 2008 to 2023. This comprehensive analysis examines the relationship between the tilt angle and latitude of the sunspot groups, as well as the correlation between the tilt angle and solar cycle strength. The methodology involves calculating tilt angles within the ±45° central meridian distance, comparing mean-based and median-based measurements, and applying specific angular separation criteria. The findings reveal that during solar cycle 24, the tilt angles increase by approximately 4° for every 10° increase in latitude, in line with Joy’s law. A significant anticorrelation is observed between the latitude-normalized tilt angle (γ/∣L∣) and solar cycle strength. The research also uncovers a substantial hemispheric asymmetry in tilt angle parameters, with the southern hemisphere (m _Joy: 0.23 ± 0.092 ∼ 0.24 ± 0.074, γ = 8.°14 ± 0.°43 ∼ 9.°04 ± 0.°486) consistently showing larger tilt angles than the northern hemisphere (m _Joy: 0.47 ± 0.096 ∼ 0.51 ± 0.062, γ = 6.°14 ± 0.°304 ∼ 6.°64 ± 0.°334).