Uncertainty-Aware Temporal Convolutional Networks for Multivariate Anomaly Detection: A Composite-Objective Framework with Chebyshev Bounds

Multivariate time-series anomaly detection on physical sensor networks faces three challenges that generic deep learning models inadequately addressed: heterogeneous sensor reliability, context-dependent anomaly scoring, and inactionable binary outputs lacking per sensor attribution. We propose an uncertainty-aware Temporal Convolutional Network (TCN) framework built on two tightly integrated uncertainty-driven components: (i) an Adaptive Uncertainty-Aware Attention (AUAA) mechanism that gates temporal attention weights by per sensor predictive uncertainty obtained from Monte Carlo dropout; and (ii) a Dynamic Weight Adapter that learns context-sensitive blending of reconstruction error and uncertainty via a GRU over weight history. The architecture also includes an exploratory per sensor attribution head, which we audit rather than claim: a controlled-perturbation test shows it is not yet causally faithful. We complement the empirical architecture with two distribution-free theoretical results: a Chebyshev-type false-positive bound on the hybrid anomaly score, and a Monte Carlo posterior moment convergence result at rate O(M−1/2). Evaluated on four-month indoor air quality sensor data, the Full Enhanced model achieves R2=0.9988 and MSE 1.65×10−4, a 25.2% MSE reduction over the Base TCN (R2=0.9984, MSE 2.20×10−4). Because the IAQ stream is unlabeled, the primary quantitative detection evaluation uses the labeled Skoltech Anomaly Benchmark (SKAB), a publicly available industrial water-circulation corpus disjoint from the IAQ training distribution; it yields an 8.8 × F1 advantage (0.477 vs. 0.054) and a 14.4 × recall advantage (0.418 vs. 0.029) for the proposed model configuration over the Base TCN at a validation-calibrated threshold applied without retuning. Against twelve established detectors under a unified protocol, the proposed model attains the best F1 and recall, while the strongest reconstruction baselines retain higher precision and a marginally higher ROC-AUC, a recall-driven trade-off. Ablation isolates each component’s contribution, the detector degrades gracefully under channel masking and noise, and the distribution-free false-positive bound is empirically respected. The framework retains a low inference cost (0.16 ms per window at M=20 Monte Carlo samples, including the uncertainty pass).