Dual-PID-Driven Adaptive Latent Factorization of Tensors for NILM Data Representation

Non-intrusive load monitoring (NILM) plays an important role in intelligent energy management systems. However, due to device failures, communication interruptions, and sensor instability, NILM data are often highly incomplete, making it difficult to obtain reliable load representations for downstream tasks. Latent factorization of tensors (LFT) provides an effective solution for NILM data representation by preserving intrinsic multidimensional structures and capturing temporal correlations. However, existing stochastic gradient descent (SGD)-based LFT models often suffer from limited optimization efficiency and representation accuracy. To address these challenges, this paper proposes a dual-proportional-integral-derivative (PID)-driven adaptive latent factorization of tensors (DPAL) model. Its main innovations include: (i) a nonlinear PID controller-driven training error regulation mechanism that exploits historical error information to improve optimization efficiency and representation accuracy; (ii) an incremental PID controller-integrated fine-grained learning rate adjustment strategy that enhances convergence speed and optimization stability; and (iii) a fuzzy logic-based adaptive gain tuning mechanism for PID controllers that improves model practicality and adaptability. Moreover, we provide a conditional coordinate-wise convergence and stability analysis under explicit smoothness and boundedness assumptions. Experimental results on three real-world NILM datasets demonstrate that the proposed DPAL model consistently outperforms state-of-the-art methods in terms of representation accuracy and computational efficiency.