Ting Mao

Accurate Remaining Useful Life (RUL) prediction is vital for industrial reliability. While deep learning methods like Temporal Convolutional Networks (TCN) have shown potential, they suffer from static convolutional kernels that fail to adaptively capture complex degradation dynamics and often ignore frequency-domain physical priors. To address these limitations, we propose a Temporal-Physics Aware Dynamic Network (TPADN). TPADN adopts a Deep-stage Decomposition Strategy that splits deep stages into an Overview-Net for global degradation context generation and a Focus-Net with one-dimensional Context-Mixing Dynamic Convolution, enabling input-dependent causal kernel generation. A physics-aware input strategy fuses raw vibration signals with their Envelope Spectrum to inject fault characteristic frequency information, while a learnable Soft Thresholding mechanism suppresses noise adaptively. Experiments on FEMTO and XJTU-SY datasets demonstrate that TPADN achieves superior accuracy and robustness compared to state-of-the-art methods.

Lithium-ion batteries have been developed as the most widely used energy storage equipment and power batteries. State-of-charge (SOC) of the battery is a key index to evaluate the remaining range of electric vehicles. The existing SOC estimation methods perform unsatisfactorily on the multivariate long-time series data produced by battery operation. In this article, a graph deviation-based autoformer is proposed to realize accurate SOC estimation. The GD-based input module utilizes the graph structure with embedding vectors to extract spatial features and detect outliers. Encoder and decoder can acquire the temporal cycle dependencies in the data, using sequence decomposition block and auto-correlation mechanism instead of self-attention mechanism. Meanwhile, the online detection method can filter out noise and fluctuations to enhance the accuracy and robustness of the estimation results. The average values of normalized root mean square error, normalized mean absolute error, and R ² achieved in the experiments are 0.0057, 0.0042, and 0.9995 respectively, which indicates superior performance on SOC estimation compared to other state-of-the-art methods. The method also has excellent generalization capability for new driving modes and new temperatures, which shows promising potential in practical applications.

Entropy measures the randomness or uncertainty of a stochastic process, and the entropy rate refers to the limit of the time average of entropy. The generalized entropy rate in the form of delayed averages can overcome the redundancy of initial information while ensuring stationarity. Therefore, it has better practical value. A Hidden Markov Model (HMM) contains two stochastic processes, a stochastic process in which all states can be observed and a Markov chain in which all states cannot be observed. The entropy rate is an important characteristic of HMMs. The transition matrix of a homogeneous HMM is unique, while a Nonhomogeneous Hidden Markov Model (NHMM) requires the transition matrices to be dependent on time variables. From the perspective of model structure, NHMMs are novel extensions of homogeneous HMMs. In this paper, the concepts of the generalized entropy rate and NHMMs are defined and fully explained, a strong limit theorem and limit properties of a norm are presented, and then generalized entropy ergodic theorems with an almost surely convergence for NHMMs are obtained. These results provide concise formulas for the computation and estimation of the generalized entropy rate for NHMMs.