Fault detection for distributed-parameter systems has predominantly been model-based, with performance heavily contingent on prior model information, which limits applicability in industrial settings. This chapter makes an initial attempt to establish a novel framework that integrates on-line systems modeling with fault detection for unknown high-dimensional distributed-parameter systems. The two components are coupled: the systems modeling error is repurposed as the residual signal for fault detection, while the on-line modeling is switched to off-line mode conditional on the detection outcomes. The high-dimensional distributed-parameter systems are first decomposed into spatial features and temporal sequences. A receding-horizon scheme is then employed to learn the temporal dynamics, and the residual signal is constructed from the temporal validation error. Experimental studies on sensor-fault diagnosis for the thermal process of a two-dimension battery cell are conducted to validate the method.